cos(3x)cos(x)=sin(3x)sin(x)

Solution for cos(3x)cos(x)=sin(3x)sin(x) equation:

Simplifying
cos(3x) * cos(x) = sin(3x) * sin(x)

Remove parenthesis around (3x)
cos * 3x * cos(x) = sin(3x) * sin(x)

Reorder the terms for easier multiplication:
3cos * x * cos * x = sin(3x) * sin(x)

Multiply cos * x
3cosx * cos * x = sin(3x) * sin(x)

Multiply cosx * cos
3c2o2s2x * x = sin(3x) * sin(x)

Multiply c2o2s2x * x
3c2o2s2x2 = sin(3x) * sin(x)

Remove parenthesis around (3x)
3c2o2s2x2 = ins * 3x * sin(x)

Reorder the terms for easier multiplication:
3c2o2s2x2 = 3ins * x * ins * x

Multiply ins * x
3c2o2s2x2 = 3insx * ins * x

Multiply insx * ins
3c2o2s2x2 = 3i2n2s2x * x

Multiply i2n2s2x * x
3c2o2s2x2 = 3i2n2s2x2

Solving
3c2o2s2x2 = 3i2n2s2x2

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Divide each side by '3o2s2x2'.
c2 = i2n2o-2

Simplifying
c2 = i2n2o-2

Take the square root of each side:
c = {-1ino-1, ino-1}