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

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


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

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

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

Multiply ins * x
4insx * ins * x = cos(4x) * cos(x)

Multiply insx * ins
4i2n2s2x * x = cos(4x) * cos(x)

Multiply i2n2s2x * x
4i2n2s2x2 = cos(4x) * cos(x)

Remove parenthesis around (4x)
4i2n2s2x2 = cos * 4x * cos(x)

Reorder the terms for easier multiplication:
4i2n2s2x2 = 4cos * x * cos * x

Multiply cos * x
4i2n2s2x2 = 4cosx * cos * x

Multiply cosx * cos
4i2n2s2x2 = 4c2o2s2x * x

Multiply c2o2s2x * x
4i2n2s2x2 = 4c2o2s2x2

Solving
4i2n2s2x2 = 4c2o2s2x2

Solving for variable 'i'.

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

Divide each side by '4n2s2x2'.
i2 = c2n-2o2

Simplifying
i2 = c2n-2o2

Take the square root of each side:
i = {-1cn-1o, cn-1o}

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