sin(2*x)*sin(6*x)=cos(x)*cos(3*x)

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Solution for sin(2*x)*sin(6*x)=cos(x)*cos(3*x) equation: 


Simplifying
sin(2x) * sin(6x) = cos(x) * cos(3x)

Remove parenthesis around (2x)
ins * 2x * sin(6x) = cos(x) * cos(3x)

Remove parenthesis around (6x)
ins * 2x * ins * 6x = cos(x) * cos(3x)

Reorder the terms for easier multiplication:
2 * 6ins * x * ins * x = cos(x) * cos(3x)

Multiply 2 * 6
12ins * x * ins * x = cos(x) * cos(3x)

Multiply ins * x
12insx * ins * x = cos(x) * cos(3x)

Multiply insx * ins
12i2n2s2x * x = cos(x) * cos(3x)

Multiply i2n2s2x * x
12i2n2s2x2 = cos(x) * cos(3x)

Remove parenthesis around (3x)
12i2n2s2x2 = cos * x * cos * 3x

Reorder the terms for easier multiplication:
12i2n2s2x2 = 3cos * x * cos * x

Multiply cos * x
12i2n2s2x2 = 3cosx * cos * x

Multiply cosx * cos
12i2n2s2x2 = 3c2o2s2x * x

Multiply c2o2s2x * x
12i2n2s2x2 = 3c2o2s2x2

Solving
12i2n2s2x2 = 3c2o2s2x2

Solving for variable 'i'.

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

Divide each side by '12n2s2x2'.
i2 = 0.25c2n-2o2

Simplifying
i2 = 0.25c2n-2o2

Take the square root of each side:
i = {-0.5cn-1o, 0.5cn-1o}

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