Sin(5x)-sin(3x)=2cos^2(2x)-1

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Solution for Sin(5x)-sin(3x)=2cos^2(2x)-1 equation: 


Simplifying
Sin(5x) + -1sin(3x) = 2cos2(2x) + -1

Remove parenthesis around (5x)
inS * 5x + -1sin(3x) = 2cos2(2x) + -1

Reorder the terms for easier multiplication:
5inS * x + -1sin(3x) = 2cos2(2x) + -1

Multiply inS * x
5inxS + -1sin(3x) = 2cos2(2x) + -1

Remove parenthesis around (3x)
5inxS + -1ins * 3x = 2cos2(2x) + -1

Reorder the terms for easier multiplication:
5inxS + -1 * 3ins * x = 2cos2(2x) + -1

Multiply -1 * 3
5inxS + -3ins * x = 2cos2(2x) + -1

Multiply ins * x
5inxS + -3insx = 2cos2(2x) + -1

Reorder the terms:
-3insx + 5inxS = 2cos2(2x) + -1

Remove parenthesis around (2x)
-3insx + 5inxS = 2cos2 * 2x + -1

Reorder the terms for easier multiplication:
-3insx + 5inxS = 2 * 2cos2 * x + -1

Multiply 2 * 2
-3insx + 5inxS = 4cos2 * x + -1

Multiply cos2 * x
-3insx + 5inxS = 4cos2x + -1

Reorder the terms:
-3insx + 5inxS = -1 + 4cos2x

Solving
-3insx + 5inxS = -1 + 4cos2x

Solving for variable 'i'.

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

Reorder the terms:
1 + -4cos2x + -3insx + 5inxS = -1 + 4cos2x + 1 + -4cos2x

Reorder the terms:
1 + -4cos2x + -3insx + 5inxS = -1 + 1 + 4cos2x + -4cos2x

Combine like terms: -1 + 1 = 0
1 + -4cos2x + -3insx + 5inxS = 0 + 4cos2x + -4cos2x
1 + -4cos2x + -3insx + 5inxS = 4cos2x + -4cos2x

Combine like terms: 4cos2x + -4cos2x = 0
1 + -4cos2x + -3insx + 5inxS = 0

The solution to this equation could not be determined.

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