Mister Exam

Lang:

Other calculators

How to use it?
Least common denominator:
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))
x+(6-x^2/1+x)/6+x/(x^2-1)
(x^2+4/x^x^2-4*x+4+x-2/2-x)/4/x^2-4
(x/216+5*3^(1/2)/144)/(7776*x-97200*3^(1/2))
Factor polynomial:
y^m+4-y^m-1+y^5-1
-y+a*y
y^4-25
y^3+x/3
Factor squared:
-y^4+5*y^2-2
y^4+5*y^2-10
y^4+4*y^2+9
y^4-4*y^2-8
How do you in partial fractions?:
(t^3+1)/(t^2-t+t)
((5x+y)/(x-5y)+(5x-y)/(x+5y)):((x^2+y^2)/(x^2-25y^2))
(4x^2-19x+12)/(x^3-64)
(3*n-1)/(5*n+4)
Identical expressions
tan(x-pi/ four)-tan(x+pi/ four)
tangent of (x minus Pi divide by 4) minus tangent of (x plus Pi divide by 4)
tangent of (x minus Pi divide by four) minus tangent of (x plus Pi divide by four)
tanx-pi/4-tanx+pi/4
tan(x-pi divide by 4)-tan(x+pi divide by 4)
Similar expressions
tan(x+pi/4)-tan(x+pi/4)
tan(x-pi/4)+tan(x+pi/4)
tan(x-pi/4)-tan(x-pi/4)
tan((x-pi)/4)-tan((x+pi)/4)

Expression simplification/ Least common denominator/ tan(x-pi/4)-tan(x+pi/4)

Least common denominator tan(x-pi/4)-tan(x+pi/4)

The solution

You have entered [src]

   /    pi\      /    pi\
tan|x - --| - tan|x + --|
   \    4 /      \    4 /

$$\tan{\left(x - \frac{\pi}{4} \right)} - \tan{\left(x + \frac{\pi}{4} \right)}$$

tan(x - pi/4) - tan(x + pi/4)

General simplification [src]

     /    pi\      /    pi\
- cot|x + --| - tan|x + --|
     \    4 /      \    4 /

$$- \tan{\left(x + \frac{\pi}{4} \right)} - \cot{\left(x + \frac{\pi}{4} \right)}$$

-cot(x + pi/4) - tan(x + pi/4)

Numerical answer [src]

-tan(x + pi/4) + tan(x - pi/4)

-tan(x + pi/4) + tan(x - pi/4)

Common denominator [src]

     /    pi\      /    pi\
- cot|x + --| - tan|x + --|
     \    4 /      \    4 /

$$- \tan{\left(x + \frac{\pi}{4} \right)} - \cot{\left(x + \frac{\pi}{4} \right)}$$

-cot(x + pi/4) - tan(x + pi/4)

Rational denominator [src]

     /    pi\      /    pi\
- cot|x + --| - tan|x + --|
     \    4 /      \    4 /

$$- \tan{\left(x + \frac{\pi}{4} \right)} - \cot{\left(x + \frac{\pi}{4} \right)}$$

-cot(x + pi/4) - tan(x + pi/4)

Powers [src]

  /     /    pi\      /     pi\\     /     /    pi\      /     pi\\
  |   I*|x - --|    I*|-x + --||     |   I*|x + --|    I*|-x - --||
  |     \    4 /      \     4 /|     |     \    4 /      \     4 /|
I*\- e           + e           /   I*\- e           + e           /
-------------------------------- - --------------------------------
      /    pi\      /     pi\            /    pi\      /     pi\   
    I*|x - --|    I*|-x + --|          I*|x + --|    I*|-x - --|   
      \    4 /      \     4 /            \    4 /      \     4 /   
   e           + e                    e           + e

$$- \frac{i \left(e^{i \left(- x - \frac{\pi}{4}\right)} - e^{i \left(x + \frac{\pi}{4}\right)}\right)}{e^{i \left(- x - \frac{\pi}{4}\right)} + e^{i \left(x + \frac{\pi}{4}\right)}} + \frac{i \left(e^{i \left(- x + \frac{\pi}{4}\right)} - e^{i \left(x - \frac{\pi}{4}\right)}\right)}{e^{i \left(- x + \frac{\pi}{4}\right)} + e^{i \left(x - \frac{\pi}{4}\right)}}$$

     /    pi\      /    pi\
- cot|x + --| - tan|x + --|
     \    4 /      \    4 /

$$- \tan{\left(x + \frac{\pi}{4} \right)} - \cot{\left(x + \frac{\pi}{4} \right)}$$

-cot(x + pi/4) - tan(x + pi/4)

Combinatorics [src]

     /    pi\      /    pi\
- cot|x + --| - tan|x + --|
     \    4 /      \    4 /

$$- \tan{\left(x + \frac{\pi}{4} \right)} - \cot{\left(x + \frac{\pi}{4} \right)}$$

-cot(x + pi/4) - tan(x + pi/4)

Combining rational expressions [src]

     /pi + 4*x\      /-pi + 4*x\
- tan|--------| + tan|---------|
     \   4    /      \    4    /

$$\tan{\left(\frac{4 x - \pi}{4} \right)} - \tan{\left(\frac{4 x + \pi}{4} \right)}$$

-tan((pi + 4*x)/4) + tan((-pi + 4*x)/4)

Expand expression [src]

    1            1          tan(x)       cot(x)  
---------- - ---------- - ---------- - ----------
1 + cot(x)   1 - tan(x)   1 - tan(x)   1 + cot(x)

$$- \frac{\cot{\left(x \right)}}{\cot{\left(x \right)} + 1} + \frac{1}{\cot{\left(x \right)} + 1} - \frac{\tan{\left(x \right)}}{1 - \tan{\left(x \right)}} - \frac{1}{1 - \tan{\left(x \right)}}$$

1/(1 + cot(x)) - 1/(1 - tan(x)) - tan(x)/(1 - tan(x)) - cot(x)/(1 + cot(x))

Trigonometric part [src]

       1             1     
- ----------- - -----------
     /    pi\      /    pi\
  cot|x + --|   tan|x + --|
     \    4 /      \    4 /

$$- \frac{1}{\cot{\left(x + \frac{\pi}{4} \right)}} - \frac{1}{\tan{\left(x + \frac{\pi}{4} \right)}}$$

       2/    pi\                 
  2*sin |x + --|                 
        \    4 /      cos(2*x)   
- -------------- - --------------
     cos(2*x)           2/    pi\
                   2*sin |x + --|
                         \    4 /

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

   /       2   \
-2*\1 + tan (x)/
----------------
         2      
  1 - tan (x)

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

       1           /    pi\
- ----------- - tan|x + --|
     /    pi\      \    4 /
  tan|x + --|              
     \    4 /

$$- \tan{\left(x + \frac{\pi}{4} \right)} - \frac{1}{\tan{\left(x + \frac{\pi}{4} \right)}}$$

     /    pi\      /    pi\
- cot|x + --| - tan|x + --|
     \    4 /      \    4 /

$$- \tan{\left(x + \frac{\pi}{4} \right)} - \cot{\left(x + \frac{\pi}{4} \right)}$$

     /    pi\      /    pi\
  sec|x + --|   csc|x + --|
     \    4 /      \    4 /
- ----------- - -----------
     /    pi\      /    pi\
  csc|x + --|   sec|x + --|
     \    4 /      \    4 /

$$- \frac{\csc{\left(x + \frac{\pi}{4} \right)}}{\sec{\left(x + \frac{\pi}{4} \right)}} - \frac{\sec{\left(x + \frac{\pi}{4} \right)}}{\csc{\left(x + \frac{\pi}{4} \right)}}$$

     -2      
-------------
   /pi      \
sin|-- + 2*x|
   \2       /

$$- \frac{2}{\sin{\left(2 x + \frac{\pi}{2} \right)}}$$

   /    3*pi\      /    pi\
cos|x - ----|   cos|x - --|
   \     4  /      \    4 /
------------- - -----------
    /    pi\       /    pi\
 sin|x + --|    cos|x + --|
    \    4 /       \    4 /

$$- \frac{\cos{\left(x - \frac{\pi}{4} \right)}}{\cos{\left(x + \frac{\pi}{4} \right)}} + \frac{\cos{\left(x - \frac{3 \pi}{4} \right)}}{\sin{\left(x + \frac{\pi}{4} \right)}}$$

     /    pi\      /    pi\
  sec|x + --|   sec|x - --|
     \    4 /      \    4 /
- ----------- - -----------
     /    pi\      /    pi\
  sec|x - --|   sec|x + --|
     \    4 /      \    4 /

$$- \frac{\sec{\left(x - \frac{\pi}{4} \right)}}{\sec{\left(x + \frac{\pi}{4} \right)}} - \frac{\sec{\left(x + \frac{\pi}{4} \right)}}{\sec{\left(x - \frac{\pi}{4} \right)}}$$

       2/    pi\        2/    pi\
  2*cos |x + --|   2*sin |x + --|
        \    4 /         \    4 /
- -------------- - --------------
     cos(2*x)         cos(2*x)

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

     /     pi\      /    pi\ 
  csc|-x + --|   csc|x + --| 
     \     4 /      \    4 / 
- ------------ - ------------
     /    pi\       /     pi\
  csc|x + --|    csc|-x + --|
     \    4 /       \     4 /

$$- \frac{\csc{\left(- x + \frac{\pi}{4} \right)}}{\csc{\left(x + \frac{\pi}{4} \right)}} - \frac{\csc{\left(x + \frac{\pi}{4} \right)}}{\csc{\left(- x + \frac{\pi}{4} \right)}}$$

-2*sec(2*x)

$$- 2 \sec{\left(2 x \right)}$$

       2/    pi\        2/    3*pi\
  2*sin |x + --|   2*sin |x + ----|
        \    4 /         \     4  /
- -------------- - ----------------
     /pi      \        /pi      \  
  sin|-- + 2*x|     sin|-- + 2*x|  
     \2       /        \2       /

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

     /    pi\      /    pi\
  cos|x + --|   sin|x + --|
     \    4 /      \    4 /
- ----------- - -----------
     /    pi\      /    pi\
  cos|x - --|   cos|x + --|
     \    4 /      \    4 /

$$- \frac{\sin{\left(x + \frac{\pi}{4} \right)}}{\cos{\left(x + \frac{\pi}{4} \right)}} - \frac{\cos{\left(x + \frac{\pi}{4} \right)}}{\cos{\left(x - \frac{\pi}{4} \right)}}$$

      /pi      \
-2*csc|-- - 2*x|
      \2       /

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

   /       2   \
-2*\1 + cot (x)/
----------------
          2     
  -1 + cot (x)

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

  -2    
--------
cos(2*x)

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

       1           /    pi\
- ----------- - cot|x + --|
     /    pi\      \    4 /
  cot|x + --|              
     \    4 /

$$- \cot{\left(x + \frac{\pi}{4} \right)} - \frac{1}{\cot{\left(x + \frac{\pi}{4} \right)}}$$

     /    pi\      /    pi\
  cos|x + --|   cos|x - --|
     \    4 /      \    4 /
- ----------- - -----------
     /    pi\      /    pi\
  cos|x - --|   cos|x + --|
     \    4 /      \    4 /

$$- \frac{\cos{\left(x - \frac{\pi}{4} \right)}}{\cos{\left(x + \frac{\pi}{4} \right)}} - \frac{\cos{\left(x + \frac{\pi}{4} \right)}}{\cos{\left(x - \frac{\pi}{4} \right)}}$$

-cos(x + pi/4)/cos(x - pi/4) - cos(x - pi/4)/cos(x + pi/4)

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator tan(x-pi/4)-tan(x+pi/4)

The solution