Mister Exam
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How to use it?
- Equation:
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Equation (x^2-1)/(x+2)=4x
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Equation 3*x+5+(x+5)=(1-x)+4
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Equation cos(x)=3/4
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Equation cos(x)=(1/2)
- Express {x} in terms of y where:
- 18*x-20*y=-7
- -13*x+7*y=11
- -19*x-14*y=-8
- 4*x+18*y=-14
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Identical expressions
- sqrt(thirty)*log(x- ten *sqrt(thirty))/ two -sqrt(thirty)*log(x+ ten *sqrt(thirty))/ two =Const-t
- square root of (30) multiply by logarithm of (x minus 10 multiply by square root of (30)) divide by 2 minus square root of (30) multiply by logarithm of (x plus 10 multiply by square root of (30)) divide by 2 equally Const minus t
- square root of (thirty) multiply by logarithm of (x minus ten multiply by square root of (thirty)) divide by two minus square root of (thirty) multiply by logarithm of (x plus ten multiply by square root of (thirty)) divide by two equally Const minus t
- √(30)*log(x-10*√(30))/2-√(30)*log(x+10*√(30))/2=Const-t
- sqrt(30)log(x-10sqrt(30))/2-sqrt(30)log(x+10sqrt(30))/2=Const-t
- sqrt30logx-10sqrt30/2-sqrt30logx+10sqrt30/2=Const-t
- sqrt(30)*log(x-10*sqrt(30)) divide by 2-sqrt(30)*log(x+10*sqrt(30)) divide by 2=Const-t
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Similar expressions
- sqrt(30)*log(x-10*sqrt(30))/2-sqrt(30)*log(x-10*sqrt(30))/2=Const-t
- sqrt(30)*log(x-10*sqrt(30))/2+sqrt(30)*log(x+10*sqrt(30))/2=Const-t
- sqrt(30)*log(x+10*sqrt(30))/2-sqrt(30)*log(x+10*sqrt(30))/2=Const-t
- sqrt(30)*log(x-10*sqrt(30))/2-sqrt(30)*log(x+10*sqrt(30))/2=Const+t
sqrt(30)*log(x-10*sqrt(30))/2-sqrt(30)*log(x+10*sqrt(30))/2=Const-t equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
____ / ____\ ____ / ____\
\/ 30 *log\x - 10*\/ 30 / \/ 30 *log\x + 10*\/ 30 /
------------------------- - ------------------------- = c - t
2 2
$$\frac{\sqrt{30} \log{\left(x - 10 \sqrt{30} \right)}}{2} - \frac{\sqrt{30} \log{\left(x + 10 \sqrt{30} \right)}}{2} = c - t$$
The graph
Rapid solution
[src]
/ ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \
____ | \/ 30 *re(t) \/ 30 *re(c)| | \/ 30 *re(t) \/ 30 *re(c)| ____ | \/ 30 *im(t) \/ 30 *im(c)| | \/ 30 *im(t) \/ 30 *im(c)|
10*\/ 30 *cosh|- ------------ + ------------|*sinh|- ------------ + ------------| 10*I*\/ 30 *cos|- ------------ + ------------|*sin|- ------------ + ------------|
\ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 /
x1 = - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \ \ / / ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \ \
| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| | | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| |
/ / ____ ____ \ / ____ ____ \\ | cos |- ------------ + ------------|*sin |- ------------ + ------------| cosh |- ------------ + ------------|*sinh |- ------------ + ------------| | / / ____ ____ \ / ____ ____ \\ | cos |- ------------ + ------------|*sin |- ------------ + ------------| cosh |- ------------ + ------------|*sinh |- ------------ + ------------| |
| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | \ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 / | | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | \ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 / |
|cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------| |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|
\ \ 30 30 / \ 30 30 // | 2 2| \ \ 30 30 / \ 30 30 // | 2 2|
|/ / ____ ____ \ / ____ ____ \\ / / ____ ____ \ / ____ ____ \\ | |/ / ____ ____ \ / ____ ____ \\ / / ____ ____ \ / ____ ____ \\ |
|| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | || 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| |
||cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| | ||cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |
\\ \ 30 30 / \ 30 30 // \ \ 30 30 / \ 30 30 // / \\ \ 30 30 / \ 30 30 // \ \ 30 30 / \ 30 30 // /
$$x_{1} = \frac{10 \sqrt{30} i \sin{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)} - \frac{10 \sqrt{30} \sinh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)}$$
x1 = 10*sqrt(30)*i*sin(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)*cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)/((sin(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2*cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2/(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2*cosh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2/(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)^2)*(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)) - 10*sqrt(30)*sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)*cosh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)/((sin(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2*cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2/(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2*cosh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2/(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2)^2)*(cos(sqrt(30)*im(c)/30 - sqrt(30)*im(t)/30)^2 + sinh(sqrt(30)*re(c)/30 - sqrt(30)*re(t)/30)^2))
Sum and product of roots
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sum
/ ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \
____ | \/ 30 *re(t) \/ 30 *re(c)| | \/ 30 *re(t) \/ 30 *re(c)| ____ | \/ 30 *im(t) \/ 30 *im(c)| | \/ 30 *im(t) \/ 30 *im(c)|
10*\/ 30 *cosh|- ------------ + ------------|*sinh|- ------------ + ------------| 10*I*\/ 30 *cos|- ------------ + ------------|*sin|- ------------ + ------------|
\ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 /
- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \ \ / / ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \ \
| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| | | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| |
/ / ____ ____ \ / ____ ____ \\ | cos |- ------------ + ------------|*sin |- ------------ + ------------| cosh |- ------------ + ------------|*sinh |- ------------ + ------------| | / / ____ ____ \ / ____ ____ \\ | cos |- ------------ + ------------|*sin |- ------------ + ------------| cosh |- ------------ + ------------|*sinh |- ------------ + ------------| |
| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | \ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 / | | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | \ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 / |
|cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------| |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|
\ \ 30 30 / \ 30 30 // | 2 2| \ \ 30 30 / \ 30 30 // | 2 2|
|/ / ____ ____ \ / ____ ____ \\ / / ____ ____ \ / ____ ____ \\ | |/ / ____ ____ \ / ____ ____ \\ / / ____ ____ \ / ____ ____ \\ |
|| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | || 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| |
||cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| | ||cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |
\\ \ 30 30 / \ 30 30 // \ \ 30 30 / \ 30 30 // / \\ \ 30 30 / \ 30 30 // \ \ 30 30 / \ 30 30 // /
$$\frac{10 \sqrt{30} i \sin{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)} - \frac{10 \sqrt{30} \sinh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)}$$
=
/ ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \
____ | \/ 30 *re(t) \/ 30 *re(c)| | \/ 30 *re(t) \/ 30 *re(c)| ____ | \/ 30 *im(t) \/ 30 *im(c)| | \/ 30 *im(t) \/ 30 *im(c)|
10*\/ 30 *cosh|- ------------ + ------------|*sinh|- ------------ + ------------| 10*I*\/ 30 *cos|- ------------ + ------------|*sin|- ------------ + ------------|
\ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 /
- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \ \ / / ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \ \
| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| | | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| |
/ / ____ ____ \ / ____ ____ \\ | cos |- ------------ + ------------|*sin |- ------------ + ------------| cosh |- ------------ + ------------|*sinh |- ------------ + ------------| | / / ____ ____ \ / ____ ____ \\ | cos |- ------------ + ------------|*sin |- ------------ + ------------| cosh |- ------------ + ------------|*sinh |- ------------ + ------------| |
| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | \ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 / | | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | \ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 / |
|cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------| |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|
\ \ 30 30 / \ 30 30 // | 2 2| \ \ 30 30 / \ 30 30 // | 2 2|
|/ / ____ ____ \ / ____ ____ \\ / / ____ ____ \ / ____ ____ \\ | |/ / ____ ____ \ / ____ ____ \\ / / ____ ____ \ / ____ ____ \\ |
|| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | || 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| |
||cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| | ||cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |
\\ \ 30 30 / \ 30 30 // \ \ 30 30 / \ 30 30 // / \\ \ 30 30 / \ 30 30 // \ \ 30 30 / \ 30 30 // /
$$\frac{10 \sqrt{30} i \sin{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)} - \frac{10 \sqrt{30} \sinh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)}$$
product
/ ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \
____ | \/ 30 *re(t) \/ 30 *re(c)| | \/ 30 *re(t) \/ 30 *re(c)| ____ | \/ 30 *im(t) \/ 30 *im(c)| | \/ 30 *im(t) \/ 30 *im(c)|
10*\/ 30 *cosh|- ------------ + ------------|*sinh|- ------------ + ------------| 10*I*\/ 30 *cos|- ------------ + ------------|*sin|- ------------ + ------------|
\ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 /
- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \ \ / / ____ ____ \ / ____ ____ \ / ____ ____ \ / ____ ____ \ \
| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| | | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| 2| \/ 30 *re(t) \/ 30 *re(c)| |
/ / ____ ____ \ / ____ ____ \\ | cos |- ------------ + ------------|*sin |- ------------ + ------------| cosh |- ------------ + ------------|*sinh |- ------------ + ------------| | / / ____ ____ \ / ____ ____ \\ | cos |- ------------ + ------------|*sin |- ------------ + ------------| cosh |- ------------ + ------------|*sinh |- ------------ + ------------| |
| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | \ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 / | | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | \ 30 30 / \ 30 30 / \ 30 30 / \ 30 30 / |
|cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------| |cos |- ------------ + ------------| + sinh |- ------------ + ------------||*|----------------------------------------------------------------------------- + -----------------------------------------------------------------------------|
\ \ 30 30 / \ 30 30 // | 2 2| \ \ 30 30 / \ 30 30 // | 2 2|
|/ / ____ ____ \ / ____ ____ \\ / / ____ ____ \ / ____ ____ \\ | |/ / ____ ____ \ / ____ ____ \\ / / ____ ____ \ / ____ ____ \\ |
|| 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | || 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| | 2| \/ 30 *im(t) \/ 30 *im(c)| 2| \/ 30 *re(t) \/ 30 *re(c)|| |
||cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| | ||cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |cos |- ------------ + ------------| + sinh |- ------------ + ------------|| |
\\ \ 30 30 / \ 30 30 // \ \ 30 30 / \ 30 30 // / \\ \ 30 30 / \ 30 30 // \ \ 30 30 / \ 30 30 // /
$$\frac{10 \sqrt{30} i \sin{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)} - \frac{10 \sqrt{30} \sinh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\frac{\sin^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}}{\left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)^{2}}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \operatorname{im}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{im}{\left(t\right)}}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \operatorname{re}{\left(c\right)}}{30} - \frac{\sqrt{30} \operatorname{re}{\left(t\right)}}{30} \right)}\right)}$$
=
/ / ____ \ \
| |\/ 30 *(-im(t) + im(c))| |
/ / ____ \ / ____ \\ |I*sin|-----------------------| / ____ \ / ____ \|
____ | 2|\/ 30 *(-im(t) + im(c))| 2|\/ 30 *(-re(t) + re(c))|| | \ 15 / |\/ 30 *(-re(t) + re(c))| |\/ 30 *(-re(t) + re(c))||
10*\/ 30 *|cos |-----------------------| + sinh |-----------------------||*|------------------------------ - cosh|-----------------------|*sinh|-----------------------||
\ \ 30 / \ 30 // \ 2 \ 30 / \ 30 //
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ____ \ / ____ \ / ____ \ / ____ \
2|\/ 30 *(-im(t) + im(c))| 2|\/ 30 *(-im(t) + im(c))| 2|\/ 30 *(-re(t) + re(c))| 2|\/ 30 *(-re(t) + re(c))|
cos |-----------------------|*sin |-----------------------| + cosh |-----------------------|*sinh |-----------------------|
\ 30 / \ 30 / \ 30 / \ 30 /
$$\frac{10 \sqrt{30} \left(\frac{i \sin{\left(\frac{\sqrt{30} \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(t\right)}\right)}{15} \right)}}{2} - \sinh{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)} \cosh{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)}\right) \left(\cos^{2}{\left(\frac{\sqrt{30} \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(t\right)}\right)}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)}\right)}{\sin^{2}{\left(\frac{\sqrt{30} \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(t\right)}\right)}{30} \right)} \cos^{2}{\left(\frac{\sqrt{30} \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(t\right)}\right)}{30} \right)} + \sinh^{2}{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)} \cosh^{2}{\left(\frac{\sqrt{30} \left(\operatorname{re}{\left(c\right)} - \operatorname{re}{\left(t\right)}\right)}{30} \right)}}$$
10*sqrt(30)*(cos(sqrt(30)*(-im(t) + im(c))/30)^2 + sinh(sqrt(30)*(-re(t) + re(c))/30)^2)*(i*sin(sqrt(30)*(-im(t) + im(c))/15)/2 - cosh(sqrt(30)*(-re(t) + re(c))/30)*sinh(sqrt(30)*(-re(t) + re(c))/30))/(cos(sqrt(30)*(-im(t) + im(c))/30)^2*sin(sqrt(30)*(-im(t) + im(c))/30)^2 + cosh(sqrt(30)*(-re(t) + re(c))/30)^2*sinh(sqrt(30)*(-re(t) + re(c))/30)^2)