Mister Exam

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Other calculators

How to use it?
Least common denominator:
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b)))/(a-b)+(2*sqrt(b))/(sqrt(a)+sqrt(b))
x/x+6*y/5-x*y-2*x^2/x^2-7*y^2/5
(x-x^3/6+x^5/120-x^7/5040)^3
(x*sqrt(4*x^2-1))/2-log(4*sqrt(4*x^2-1)+8*x)/4
Factor polynomial:
x-x+10-x^2+10
x^m-y^n+b*x-t*z+y*z+m*n
x*m*5+x*y^5-y*m*5-y6
x*a^2+x^2*a*b+b^2+x^2*b^2
Factor squared:
-y^2+y-6
-y^2+y+5
y^2-y+3
-y^2+9*y*x-x^2
How do you in partial fractions?:
1/(x^3-1)^2
5/(p^3+2*p^2+4*p-2)
((5+4/p)*((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4)))/((((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))+(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4))+1))*1/(1-((5+4/p)*((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4))*3/(2p^4+p^3+2p+3p+5)*(4/(p+4)))/(((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))+(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4))+1))
(288*t^8-864*t^7+576*t^6+576*t^5-864*t^4+288*t^3)/(t-1)^10+((-576*t^7)+1536*t^6-960*t^5-576*t^4+768*t^3-192*t^2)/(t-1)^9+(316*t^6-756*t^5+464*t^4+104*t^3-156*t^2+28*t)/(t-1)^8+(1-27*t^2)/(t-1)^4
Identical expressions
tan(two *c)*tan(two)+cos(- three *pi/ four)^(two)-sin(pi)^(two)/ two -cos(pi)^(two)/ two
tangent of (2 multiply by c) multiply by tangent of (2) plus co sinus of e of ( minus 3 multiply by Pi divide by 4) to the power of (2) minus sinus of ( Pi ) to the power of (2) divide by 2 minus co sinus of e of ( Pi ) to the power of (2) divide by 2
tangent of (two multiply by c) multiply by tangent of (two) plus co sinus of e of ( minus three multiply by Pi divide by four) to the power of (two) minus sinus of ( Pi ) to the power of (two) divide by two minus co sinus of e of ( Pi ) to the power of (two) divide by two
tan(2*c)*tan(2)+cos(-3*pi/4)(2)-sin(pi)(2)/2-cos(pi)(2)/2
tan2*c*tan2+cos-3*pi/42-sinpi2/2-cospi2/2
tan(2c)tan(2)+cos(-3pi/4)^(2)-sin(pi)^(2)/2-cos(pi)^(2)/2
tan(2c)tan(2)+cos(-3pi/4)(2)-sin(pi)(2)/2-cos(pi)(2)/2
tan2ctan2+cos-3pi/42-sinpi2/2-cospi2/2
tan2ctan2+cos-3pi/4^2-sinpi^2/2-cospi^2/2
tan(2*c)*tan(2)+cos(-3*pi divide by 4)^(2)-sin(pi)^(2) divide by 2-cos(pi)^(2) divide by 2
Similar expressions
tan(2*c)*tan(2)+cos(-3*pi/4)^(2)+sin(pi)^(2)/2-cos(pi)^(2)/2
tan(2*c)*tan(2)+cos(-3*pi/4)^(2)-sin(pi)^(2)/2+cos(pi)^(2)/2
tan(2*c)*tan(2)-cos(-3*pi/4)^(2)-sin(pi)^(2)/2-cos(pi)^(2)/2
tan(2*c)*tan(2)+cos(3*pi/4)^(2)-sin(pi)^(2)/2-cos(pi)^(2)/2

Expression simplification/ Least common denominator/ tan(2*c)*tan(2)+cos(-3*pi/4)^(2)-sin(pi)^(2)/2-cos(pi)^(2)/2

Least common denominator tan(2c)tan(2)+cos(-3*pi/4)^(2)-sin(pi)^(2)/2-cos(pi)^(2)/2

The solution

You have entered [src]

                                   2          2    
                     2/-3*pi\   sin (pi)   cos (pi)
tan(2*c)*tan(2) + cos |-----| - -------- - --------
                      \  4  /      2          2

$$\left(\left(\tan{\left(2 \right)} \tan{\left(2 c \right)} + \cos^{2}{\left(\frac{\left(-1\right) 3 \pi}{4} \right)}\right) - \frac{\sin^{2}{\left(\pi \right)}}{2}\right) - \frac{\cos^{2}{\left(\pi \right)}}{2}$$

tan(2*c)*tan(2) + cos((-3*pi)/4)^2 - sin(pi)^2/2 - cos(pi)^2/2

General simplification [src]

tan(2)*tan(2*c)

$$\tan{\left(2 \right)} \tan{\left(2 c \right)}$$

tan(2)*tan(2*c)

Combining rational expressions [src]

tan(2)*tan(2*c)

$$\tan{\left(2 \right)} \tan{\left(2 c \right)}$$

tan(2)*tan(2*c)

Combinatorics [src]

tan(2)*tan(2*c)

$$\tan{\left(2 \right)} \tan{\left(2 c \right)}$$

tan(2)*tan(2*c)

Powers [src]

tan(2)*tan(2*c)

$$\tan{\left(2 \right)} \tan{\left(2 c \right)}$$

                          2                                        
      / -3*pi*I    3*pi*I\                                         
      | -------    ------|                                         
      |    4         4   |    /   2*I    -2*I\ /   2*I*c    -2*I*c\
  1   |e          e      |    \- e    + e    /*\- e      + e      /
- - + |-------- + -------|  - -------------------------------------
  2   \   2          2   /      / -2*I    2*I\ / -2*I*c    2*I*c\  
                                \e     + e   /*\e       + e     /

$$- \frac{\left(e^{- 2 i} - e^{2 i}\right) \left(- e^{2 i c} + e^{- 2 i c}\right)}{\left(e^{- 2 i} + e^{2 i}\right) \left(e^{2 i c} + e^{- 2 i c}\right)} - \frac{1}{2} + \left(\frac{e^{- \frac{3 i \pi}{4}}}{2} + \frac{e^{\frac{3 i \pi}{4}}}{2}\right)^{2}$$

-1/2 + (exp(-3*pi*i/4)/2 + exp(3*pi*i/4)/2)^2 - (-exp(2*i) + exp(-2*i))*(-exp(2*i*c) + exp(-2*i*c))/((exp(-2*i) + exp(2*i))*(exp(-2*i*c) + exp(2*i*c)))

Rational denominator [src]

tan(2)*tan(2*c)

$$\tan{\left(2 \right)} \tan{\left(2 c \right)}$$

tan(2)*tan(2*c)

Common denominator [src]

       2          2                      
1   cos (pi)   sin (pi)                  
- - -------- - -------- + tan(2)*tan(2*c)
2      2          2

$$\tan{\left(2 \right)} \tan{\left(2 c \right)} - \frac{\cos^{2}{\left(\pi \right)}}{2} - \frac{\sin^{2}{\left(\pi \right)}}{2} + \frac{1}{2}$$

1/2 - cos(pi)^2/2 - sin(pi)^2/2 + tan(2)*tan(2*c)

Numerical answer [src]

1.11022302462516e-16 - 2.18503986326152*tan(2*c)

1.11022302462516e-16 - 2.18503986326152*tan(2*c)

Expand expression [src]

            4*tan(1)*tan(c)            
---------------------------------------
       2         2         2       2   
1 - tan (1) - tan (c) + tan (1)*tan (c)

$$\frac{4 \tan{\left(1 \right)} \tan{\left(c \right)}}{- \tan^{2}{\left(c \right)} + \tan^{2}{\left(1 \right)} \tan^{2}{\left(c \right)} - \tan^{2}{\left(1 \right)} + 1}$$

4*tan(1)*tan(c)/(1 - tan(1)^2 - tan(c)^2 + tan(1)^2*tan(c)^2)

Assemble expression [src]

                 2          2                      
   2/-3*pi\   cos (pi)   sin (pi)                  
cos |-----| - -------- - -------- + tan(2)*tan(2*c)
    \  4  /      2          2

$$\tan{\left(2 \right)} \tan{\left(2 c \right)} - \frac{\cos^{2}{\left(\pi \right)}}{2} - \frac{\sin^{2}{\left(\pi \right)}}{2} + \cos^{2}{\left(\frac{\left(-1\right) 3 \pi}{4} \right)}$$

cos((-3*pi)/4)^2 - cos(pi)^2/2 - sin(pi)^2/2 + tan(2)*tan(2*c)

Trigonometric part [src]

sin(2)*sin(2*c)
---------------
cos(2)*cos(2*c)

$$\frac{\sin{\left(2 \right)} \sin{\left(2 c \right)}}{\cos{\left(2 \right)} \cos{\left(2 c \right)}}$$

      2       2    /       2   \ /       2     \
16*tan (1)*tan (c)*\1 + tan (2)/*\1 + tan (2*c)/
------------------------------------------------
              2              2                  
 /       2   \  /       2   \                   
 \1 + tan (1)/ *\1 + tan (c)/ *tan(2)*tan(2*c)

$$\frac{16 \left(1 + \tan^{2}{\left(2 \right)}\right) \left(\tan^{2}{\left(2 c \right)} + 1\right) \tan^{2}{\left(1 \right)} \tan^{2}{\left(c \right)}}{\left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \left(\tan^{2}{\left(c \right)} + 1\right)^{2} \tan{\left(2 \right)} \tan{\left(2 c \right)}}$$

     2/    pi\    2/      pi\
4*cos |2 - --|*cos |2*c - --|
      \    2 /     \      2 /
-----------------------------
     /    pi\    /      pi\  
  cos|4 - --|*cos|4*c - --|  
     \    2 /    \      2 /

$$\frac{4 \cos^{2}{\left(2 - \frac{\pi}{2} \right)} \cos^{2}{\left(2 c - \frac{\pi}{2} \right)}}{\cos{\left(4 - \frac{\pi}{2} \right)} \cos{\left(4 c - \frac{\pi}{2} \right)}}$$

     2/pi\      /    pi\    /      pi\
  cos |--|   cos|2 - --|*cos|2*c - --|
      \2 /      \    2 /    \      2 /
- -------- + -------------------------
     2            cos(2)*cos(2*c)

$$- \frac{\cos^{2}{\left(\frac{\pi}{2} \right)}}{2} + \frac{\cos{\left(2 - \frac{\pi}{2} \right)} \cos{\left(2 c - \frac{\pi}{2} \right)}}{\cos{\left(2 \right)} \cos{\left(2 c \right)}}$$

  /        ___\                
2*\3 - 2*\/ 2 /*tan(2)*tan(2*c)
-------------------------------
                     2         
         /       ___\          
         \-2 + \/ 2 /

$$\frac{2 \left(3 - 2 \sqrt{2}\right) \tan{\left(2 \right)} \tan{\left(2 c \right)}}{\left(-2 + \sqrt{2}\right)^{2}}$$

      2       2    /       2   \ /       2     \
16*cot (1)*cot (c)*\1 + cot (2)/*\1 + cot (2*c)/
------------------------------------------------
              2              2                  
 /       2   \  /       2   \                   
 \1 + cot (1)/ *\1 + cot (c)/ *cot(2)*cot(2*c)

$$\frac{16 \left(\cot^{2}{\left(2 \right)} + 1\right) \left(\cot^{2}{\left(2 c \right)} + 1\right) \cot^{2}{\left(1 \right)} \cot^{2}{\left(c \right)}}{\left(\cot^{2}{\left(1 \right)} + 1\right)^{2} \left(\cot^{2}{\left(c \right)} + 1\right)^{2} \cot{\left(2 \right)} \cot{\left(2 c \right)}}$$

     sec(2)*sec(2*c)     
-------------------------
   /    pi\    /      pi\
sec|2 - --|*sec|2*c - --|
   \    2 /    \      2 /

$$\frac{\sec{\left(2 \right)} \sec{\left(2 c \right)}}{\sec{\left(2 - \frac{\pi}{2} \right)} \sec{\left(2 c - \frac{\pi}{2} \right)}}$$

                         2                  
      /                2\                   
      |     /      ___\ |                   
  1   \-1 + \1 - \/ 2 / /           1       
- - + -------------------- + ---------------
  2                     2    cot(2)*cot(2*c)
      /               2\                    
      |    /      ___\ |                    
      \1 + \1 - \/ 2 / /

$$- \frac{1}{2} + \frac{\left(-1 + \left(1 - \sqrt{2}\right)^{2}\right)^{2}}{\left(\left(1 - \sqrt{2}\right)^{2} + 1\right)^{2}} + \frac{1}{\cot{\left(2 \right)} \cot{\left(2 c \right)}}$$

         /        ___\       
       2*\3 - 2*\/ 2 /       
-----------------------------
            2                
/       ___\                 
\-2 + \/ 2 / *cot(2)*cot(2*c)

$$\frac{2 \left(3 - 2 \sqrt{2}\right)}{\left(-2 + \sqrt{2}\right)^{2} \cot{\left(2 \right)} \cot{\left(2 c \right)}}$$

4*csc(4)*csc(4*c)
-----------------
   2       2     
csc (2)*csc (2*c)

$$\frac{4 \csc{\left(4 \right)} \csc{\left(4 c \right)}}{\csc^{2}{\left(2 \right)} \csc^{2}{\left(2 c \right)}}$$

sec(2)*sec(2*c)
---------------
csc(2)*csc(2*c)

$$\frac{\sec{\left(2 \right)} \sec{\left(2 c \right)}}{\csc{\left(2 \right)} \csc{\left(2 c \right)}}$$

     2       2      /        ___\
8*sin (2)*sin (2*c)*\3 - 2*\/ 2 /
---------------------------------
              2                  
  /       ___\                   
  \-2 + \/ 2 / *sin(4)*sin(4*c)

$$\frac{8 \left(3 - 2 \sqrt{2}\right) \sin^{2}{\left(2 \right)} \sin^{2}{\left(2 c \right)}}{\left(-2 + \sqrt{2}\right)^{2} \sin{\left(4 \right)} \sin{\left(4 c \right)}}$$

   /    pi\    /      pi\
cos|2 - --|*cos|2*c - --|
   \    2 /    \      2 /
-------------------------
     cos(2)*cos(2*c)

$$\frac{\cos{\left(2 - \frac{\pi}{2} \right)} \cos{\left(2 c - \frac{\pi}{2} \right)}}{\cos{\left(2 \right)} \cos{\left(2 c \right)}}$$

                2/3*pi\                      
             sin |----|        2       2     
   2/-pi \       \ 2  /   4*sin (2)*sin (2*c)
sin |----| - ---------- + -------------------
    \ 4  /       2          sin(4)*sin(4*c)

$$\frac{4 \sin^{2}{\left(2 \right)} \sin^{2}{\left(2 c \right)}}{\sin{\left(4 \right)} \sin{\left(4 c \right)}} - \frac{\sin^{2}{\left(\frac{3 \pi}{2} \right)}}{2} + \sin^{2}{\left(- \frac{\pi}{4} \right)}$$

     2                   
4*sin (2)*csc(4)*csc(4*c)
-------------------------
           2             
        csc (2*c)

$$\frac{4 \sin^{2}{\left(2 \right)} \csc{\left(4 \right)} \csc{\left(4 c \right)}}{\csc^{2}{\left(2 c \right)}}$$

     /    pi\    /      pi\
4*sec|4 - --|*sec|4*c - --|
     \    2 /    \      2 /
---------------------------
   2/    pi\    2/      pi\
sec |2 - --|*sec |2*c - --|
    \    2 /     \      2 /

$$\frac{4 \sec{\left(4 - \frac{\pi}{2} \right)} \sec{\left(4 c - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 - \frac{\pi}{2} \right)} \sec^{2}{\left(2 c - \frac{\pi}{2} \right)}}$$

                     2                            
               16*tan (1)*sin(2*c)                
--------------------------------------------------
             2                                    
/       2   \                                     
\1 + tan (1)/ *(-sin(2*(-2 + c)) + sin(2*(2 + c)))

$$\frac{16 \sin{\left(2 c \right)} \tan^{2}{\left(1 \right)}}{\left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \left(- \sin{\left(2 \left(c - 2\right) \right)} + \sin{\left(2 \left(c + 2\right) \right)}\right)}$$

tan(2)*tan(2*c)

$$\tan{\left(2 \right)} \tan{\left(2 c \right)}$$

      1             sec(2)*sec(2*c)     
- ---------- + -------------------------
       2/pi\      /    pi\    /      pi\
  2*sec |--|   sec|2 - --|*sec|2*c - --|
        \2 /      \    2 /    \      2 /

$$\frac{\sec{\left(2 \right)} \sec{\left(2 c \right)}}{\sec{\left(2 - \frac{\pi}{2} \right)} \sec{\left(2 c - \frac{\pi}{2} \right)}} - \frac{1}{2 \sec^{2}{\left(\frac{\pi}{2} \right)}}$$

nan

$$\text{NaN}$$

       1       
---------------
cot(2)*cot(2*c)

$$\frac{1}{\cot{\left(2 \right)} \cot{\left(2 c \right)}}$$

      /        ___\                    
    2*\3 - 2*\/ 2 /*sec(2)*sec(2*c)    
---------------------------------------
            2                          
/       ___\     /    pi\    /      pi\
\-2 + \/ 2 / *sec|2 - --|*sec|2*c - --|
                 \    2 /    \      2 /

$$\frac{2 \left(3 - 2 \sqrt{2}\right) \sec{\left(2 \right)} \sec{\left(2 c \right)}}{\left(-2 + \sqrt{2}\right)^{2} \sec{\left(2 - \frac{\pi}{2} \right)} \sec{\left(2 c - \frac{\pi}{2} \right)}}$$

     2       2     
4*sin (2)*sin (2*c)
-------------------
  sin(4)*sin(4*c)

$$\frac{4 \sin^{2}{\left(2 \right)} \sin^{2}{\left(2 c \right)}}{\sin{\left(4 \right)} \sin{\left(4 c \right)}}$$

  /        ___\    /    pi\    /      pi\
2*\3 - 2*\/ 2 /*cos|2 - --|*cos|2*c - --|
                   \    2 /    \      2 /
-----------------------------------------
                  2                      
      /       ___\                       
      \-2 + \/ 2 / *cos(2)*cos(2*c)

$$\frac{2 \left(3 - 2 \sqrt{2}\right) \cos{\left(2 - \frac{\pi}{2} \right)} \cos{\left(2 c - \frac{\pi}{2} \right)}}{\left(-2 + \sqrt{2}\right)^{2} \cos{\left(2 \right)} \cos{\left(2 c \right)}}$$

   /     pi\    /pi      \
csc|-2 + --|*csc|-- - 2*c|
   \     2 /    \2       /
--------------------------
     csc(2)*csc(2*c)

$$\frac{\csc{\left(-2 + \frac{\pi}{2} \right)} \csc{\left(- 2 c + \frac{\pi}{2} \right)}}{\csc{\left(2 \right)} \csc{\left(2 c \right)}}$$

-cos(2*(1 + c)) + cos(2*(-1 + c))
---------------------------------
 cos(2*(1 + c)) + cos(2*(-1 + c))

$$\frac{\cos{\left(2 \left(c - 1\right) \right)} - \cos{\left(2 \left(c + 1\right) \right)}}{\cos{\left(2 \left(c - 1\right) \right)} + \cos{\left(2 \left(c + 1\right) \right)}}$$

  /        ___\    /     pi\    /pi      \
2*\3 - 2*\/ 2 /*csc|-2 + --|*csc|-- - 2*c|
                   \     2 /    \2       /
------------------------------------------
                  2                       
      /       ___\                        
      \-2 + \/ 2 / *csc(2)*csc(2*c)

$$\frac{2 \left(3 - 2 \sqrt{2}\right) \csc{\left(-2 + \frac{\pi}{2} \right)} \csc{\left(- 2 c + \frac{\pi}{2} \right)}}{\left(-2 + \sqrt{2}\right)^{2} \csc{\left(2 \right)} \csc{\left(2 c \right)}}$$

2*(3 - 2*sqrt(2))*csc(-2 + pi/2)*csc(pi/2 - 2*c)/((-2 + sqrt(2))^2*csc(2)*csc(2*c))

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator tan(2*c)*tan(2)+cos(-3*pi/4)^(2)-sin(pi)^(2)/2-cos(pi)^(2)/2

The solution

Least common denominator tan(2c)tan(2)+cos(-3*pi/4)^(2)-sin(pi)^(2)/2-cos(pi)^(2)/2