Mister Exam
Other calculators
-
How to use it?
- How do you in partial fractions?:
- z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
- sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
- sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2))
- 3/(x^3+5)-9*x^3/(x^3+5)^2
- Factor polynomial:
- x^4+1
- x^3-1^3+3^3-x^3
- y^2/2+y^23/23
- -x^7+x^6/4+9*x*5/8-9*x^4/32-x^3/8+x^2/32
- Least common denominator:
- (a+1/a+2)/a+1
- 1/(1+x^2/3)
- (z/x-z+x+z/z)/x/x^2-z^2
- (z/x-z+x+z/z)/x/x^2-x*z^2
- Factor squared:
- y^4-y^2-3
- x^2+x-2
- y^2-4*y+3
- x^2+x-3
- Graphing y =:
- 1/(cos(x)^2)
- Integral of d{x}:
- 1/(cos(x)^2)
- Derivative of:
-
1/(cos(x)^2)
-
Identical expressions
- one /(cos(x)^ two)
- 1 divide by ( co sinus of e of (x) squared )
- one divide by ( co sinus of e of (x) to the power of two)
- 1/(cos(x)2)
- 1/cosx2
- 1/(cos(x)²)
- 1/(cos(x) to the power of 2)
- 1/cosx^2
- 1 divide by (cos(x)^2)
-
Similar expressions
- 1/(cosx^2)
How do you 1/(cos(x)^2) in partial fractions?
The solution
Fraction decomposition
[src]
cos(x)^(-2)
$$\frac{1}{\cos^{2}{\left(x \right)}}$$
1 ------- 2 cos (x)
Powers
[src]
1
---------------
2
/ I*x -I*x\
|e e |
|---- + -----|
\ 2 2 /
$$\frac{1}{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}$$
(exp(i*x)/2 + exp(-i*x)/2)^(-2)
Trigonometric part
[src]
2
/ 2/x\\
|1 + tan |-||
\ \2//
--------------
2
/ 2/x\\
|1 - tan |-||
\ \2//
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}$$
2
/ 2/x\\
|1 + cot |-||
\ \2//
---------------
2
/ 2/x\\
|-1 + cot |-||
\ \2//
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}$$
2/pi \
csc |-- - x|
\2 /
$$\csc^{2}{\left(- x + \frac{\pi}{2} \right)}$$
2
----------------
2
-1 + cot (x)
1 + ------------
2
1 + cot (x)
$$\frac{2}{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1}$$
2 ------------ 1 + cos(2*x)
$$\frac{2}{\cos{\left(2 x \right)} + 1}$$
2
-----------------
/pi \
1 + sin|-- + 2*x|
\2 /
$$\frac{2}{\sin{\left(2 x + \frac{\pi}{2} \right)} + 1}$$
2
------------
1
1 + --------
sec(2*x)
$$\frac{2}{1 + \frac{1}{\sec{\left(2 x \right)}}}$$
2
---------------
2
1 - tan (x)
1 + -----------
2
1 + tan (x)
$$\frac{2}{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1}$$
2 sec (x)
$$\sec^{2}{\left(x \right)}$$
1
------------
2/ pi\
sin |x + --|
\ 2 /
$$\frac{1}{\sin^{2}{\left(x + \frac{\pi}{2} \right)}}$$
2
-----------------
1
1 + -------------
/pi \
csc|-- - 2*x|
\2 /
$$\frac{2}{1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}}$$
2/(1 + 1/csc(pi/2 - 2*x))