cos(2x)cos(x)=sin(4x)sin(x)

Solution for cos(2x)cos(x)=sin(4x)sin(x) equation:

Simplifying
cos(2x) * cos(x) = sin(4x) * sin(x)

Remove parenthesis around (2x)
cos * 2x * cos(x) = sin(4x) * sin(x)

Reorder the terms for easier multiplication:
2cos * x * cos * x = sin(4x) * sin(x)

Multiply cos * x
2cosx * cos * x = sin(4x) * sin(x)

Multiply cosx * cos
2c2o2s2x * x = sin(4x) * sin(x)

Multiply c2o2s2x * x
2c2o2s2x2 = sin(4x) * sin(x)

Remove parenthesis around (4x)
2c2o2s2x2 = ins * 4x * sin(x)

Reorder the terms for easier multiplication:
2c2o2s2x2 = 4ins * x * ins * x

Multiply ins * x
2c2o2s2x2 = 4insx * ins * x

Multiply insx * ins
2c2o2s2x2 = 4i2n2s2x * x

Multiply i2n2s2x * x
2c2o2s2x2 = 4i2n2s2x2

Solving
2c2o2s2x2 = 4i2n2s2x2

Solving for variable 'c'.

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

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

Simplifying
c2 = 2i2n2o-2

Take the square root of each side:
c = {-1.414213562ino-1, 1.414213562ino-1}