sin(5x)=sin(2x)cos(3x)

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Solution for sin(5x)=sin(2x)cos(3x) equation:


Simplifying
sin(5x) = sin(2x) * cos(3x)

Remove parenthesis around (5x)
ins * 5x = sin(2x) * cos(3x)

Reorder the terms for easier multiplication:
5ins * x = sin(2x) * cos(3x)

Multiply ins * x
5insx = sin(2x) * cos(3x)

Remove parenthesis around (2x)
5insx = ins * 2x * cos(3x)

Remove parenthesis around (3x)
5insx = ins * 2x * cos * 3x

Reorder the terms for easier multiplication:
5insx = 2 * 3ins * x * cos * x

Multiply 2 * 3
5insx = 6ins * x * cos * x

Multiply ins * x
5insx = 6insx * cos * x

Multiply insx * cos
5insx = 6cinos2x * x

Multiply cinos2x * x
5insx = 6cinos2x2

Solving
5insx = 6cinos2x2

Solving for variable 'i'.

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

Add '-6cinos2x2' to each side of the equation.
-6cinos2x2 + 5insx = 6cinos2x2 + -6cinos2x2

Combine like terms: 6cinos2x2 + -6cinos2x2 = 0
-6cinos2x2 + 5insx = 0

Factor out the Greatest Common Factor (GCF), 'insx'.
insx(-6cosx + 5) = 0

Subproblem 1

Set the factor 'insx' equal to zero and attempt to solve: Simplifying insx = 0 Solving insx = 0 Move all terms containing i to the left, all other terms to the right. Simplifying insx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-6cosx + 5)' equal to zero and attempt to solve: Simplifying -6cosx + 5 = 0 Reorder the terms: 5 + -6cosx = 0 Solving 5 + -6cosx = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6cosx = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6cosx = 0 + -5 -6cosx = 0 + -5 Combine like terms: 0 + -5 = -5 -6cosx = -5 Add '6cosx' to each side of the equation. -6cosx + 6cosx = -5 + 6cosx Combine like terms: -6cosx + 6cosx = 0 0 = -5 + 6cosx Simplifying 0 = -5 + 6cosx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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