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

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


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

Remove parenthesis around (2x)
ins * x * ins * 2x = cos(x) * cos(2x)

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

Multiply ins * x
2insx * ins * x = cos(x) * cos(2x)

Multiply insx * ins
2i2n2s2x * x = cos(x) * cos(2x)

Multiply i2n2s2x * x
2i2n2s2x2 = cos(x) * cos(2x)

Remove parenthesis around (2x)
2i2n2s2x2 = cos * x * cos * 2x

Reorder the terms for easier multiplication:
2i2n2s2x2 = 2cos * x * cos * x

Multiply cos * x
2i2n2s2x2 = 2cosx * cos * x

Multiply cosx * cos
2i2n2s2x2 = 2c2o2s2x * x

Multiply c2o2s2x * x
2i2n2s2x2 = 2c2o2s2x2

Solving
2i2n2s2x2 = 2c2o2s2x2

Solving for variable 'i'.

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

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

Simplifying
i2 = c2n-2o2

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

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