sin(3)+sin(5x)=sin(2x)+sin(6x)

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Solution for sin(3)+sin(5x)=sin(2x)+sin(6x) equation:


Simplifying
sin(3) + sin(5x) = sin(2x) + sin(6x)

Reorder the terms for easier multiplication:
3ins + sin(5x) = sin(2x) + sin(6x)

Remove parenthesis around (5x)
3ins + ins * 5x = sin(2x) + sin(6x)

Reorder the terms for easier multiplication:
3ins + 5ins * x = sin(2x) + sin(6x)

Multiply ins * x
3ins + 5insx = sin(2x) + sin(6x)

Remove parenthesis around (2x)
3ins + 5insx = ins * 2x + sin(6x)

Reorder the terms for easier multiplication:
3ins + 5insx = 2ins * x + sin(6x)

Multiply ins * x
3ins + 5insx = 2insx + sin(6x)

Remove parenthesis around (6x)
3ins + 5insx = 2insx + ins * 6x

Reorder the terms for easier multiplication:
3ins + 5insx = 2insx + 6ins * x

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

Combine like terms: 2insx + 6insx = 8insx
3ins + 5insx = 8insx

Solving
3ins + 5insx = 8insx

Solving for variable 'i'.

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

Add '-8insx' to each side of the equation.
3ins + 5insx + -8insx = 8insx + -8insx

Combine like terms: 5insx + -8insx = -3insx
3ins + -3insx = 8insx + -8insx

Combine like terms: 8insx + -8insx = 0
3ins + -3insx = 0

Factor out the Greatest Common Factor (GCF), '3ins'.
3ins(1 + -1x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'ins' equal to zero and attempt to solve: Simplifying ins = 0 Solving ins = 0 Move all terms containing i to the left, all other terms to the right. Simplifying ins = 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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