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Least common denominator:
(z+t)/(t-z)-(t-z)/(t+z)
(z/t-t/z)*5*t*z/z-t
(z*sqrt(z^2-a^2))/2-(a^2*log(2*sqrt(z^2-a^2)+2*z))/2
(z/40+1/20)*(z/40+4/5)*z
Factor polynomial:
x^3+27
x^2-x+5
x^6-x^4*y^2-x^3+x^2*y
x^6-x^2*y^4
Factor squared:
y^4+y^2+1
-y^4+y^2+4
y^4+y^2-4
-y^4+y^2+3
How do you in partial fractions?:
2*(-1+(-1+x)/(2+x))/(2+x)^2
2/(a+2)+(a-2)/(a^2+4*a+4)/(a/(2*a-4)+(a^2+4)/(8-2*a)-2/(2*a+a^2))
(4*a^3)^2*(3*b^3)^4/(12*a^2*b^4)^3
exp(-x)/(1+exp(-x))^2
Identical expressions
sin(a)^(two)+cos(pi/ three -a)*cos(pi/ three +a)
sinus of (a) to the power of (2) plus co sinus of e of ( Pi divide by 3 minus a) multiply by co sinus of e of ( Pi divide by 3 plus a)
sinus of (a) to the power of (two) plus co sinus of e of ( Pi divide by three minus a) multiply by co sinus of e of ( Pi divide by three plus a)
sin(a)(2)+cos(pi/3-a)*cos(pi/3+a)
sina2+cospi/3-a*cospi/3+a
sin(a)^(2)+cos(pi/3-a)cos(pi/3+a)
sin(a)(2)+cos(pi/3-a)cos(pi/3+a)
sina2+cospi/3-acospi/3+a
sina^2+cospi/3-acospi/3+a
sin(a)^(2)+cos(pi divide by 3-a)*cos(pi divide by 3+a)
Similar expressions
sin(a)^(2)+cos(pi/3-a)*cos(pi/3-a)
sin(a)^(2)+cos(pi/3+a)*cos(pi/3+a)
sin(a)^(2)-cos(pi/3-a)*cos(pi/3+a)

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

Least common denominator sin(a)^(2)+cos(pi/3-a)*cos(pi/3+a)

The solution

You have entered [src]

   2         /pi    \    /pi    \
sin (a) + cos|-- - a|*cos|-- + a|
             \3     /    \3     /

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

sin(a)^2 + cos(pi/3 - a)*cos(pi/3 + a)

General simplification [src]

1/4

$$\frac{1}{4}$$

1/4

Powers [src]

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

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

   2         /    pi\    /    pi\
sin (a) + cos|a + --|*sin|a + --|
             \    3 /    \    6 /

$$\sin^{2}{\left(a \right)} + \sin{\left(a + \frac{\pi}{6} \right)} \cos{\left(a + \frac{\pi}{3} \right)}$$

sin(a)^2 + cos(a + pi/3)*sin(a + pi/6)

Common denominator [src]

   2         /    pi\    /    pi\
sin (a) + cos|a + --|*sin|a + --|
             \    3 /    \    6 /

$$\sin^{2}{\left(a \right)} + \sin{\left(a + \frac{\pi}{6} \right)} \cos{\left(a + \frac{\pi}{3} \right)}$$

sin(a)^2 + cos(a + pi/3)*sin(a + pi/6)

Combinatorics [src]

   2         /    pi\    /    pi\
sin (a) + cos|a + --|*sin|a + --|
             \    3 /    \    6 /

$$\sin^{2}{\left(a \right)} + \sin{\left(a + \frac{\pi}{6} \right)} \cos{\left(a + \frac{\pi}{3} \right)}$$

sin(a)^2 + cos(a + pi/3)*sin(a + pi/6)

Numerical answer [src]

sin(a)^2 + cos(pi/3 + a)*cos(pi/3 - a)

sin(a)^2 + cos(pi/3 + a)*cos(pi/3 - a)

Rational denominator [src]

   2         /    pi\    /    pi\
sin (a) + cos|a + --|*cos|a - --|
             \    3 /    \    3 /

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

sin(a)^2 + cos(a + pi/3)*cos(a - pi/3)

Combining rational expressions [src]

   2         /pi - 3*a\    /pi + 3*a\
sin (a) + cos|--------|*cos|--------|
             \   3    /    \   3    /

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

sin(a)^2 + cos((pi - 3*a)/3)*cos((pi + 3*a)/3)

Expand expression [src]

   2         2   
cos (a)   sin (a)
------- + -------
   4         4

$$\frac{\sin^{2}{\left(a \right)}}{4} + \frac{\cos^{2}{\left(a \right)}}{4}$$

cos(a)^2/4 + sin(a)^2/4

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Identical expressions

Similar expressions

Least common denominator sin(a)^(2)+cos(pi/3-a)*cos(pi/3+a)

The solution