sin(8x)-sin(2x)=Sin(3x)

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Solution for sin(8x)-sin(2x)=Sin(3x) equation:


Simplifying
sin(8x) + -1sin(2x) = Sin(3x)

Remove parenthesis around (8x)
ins * 8x + -1sin(2x) = Sin(3x)

Reorder the terms for easier multiplication:
8ins * x + -1sin(2x) = Sin(3x)

Multiply ins * x
8insx + -1sin(2x) = Sin(3x)

Remove parenthesis around (2x)
8insx + -1ins * 2x = Sin(3x)

Reorder the terms for easier multiplication:
8insx + -1 * 2ins * x = Sin(3x)

Multiply -1 * 2
8insx + -2ins * x = Sin(3x)

Multiply ins * x
8insx + -2insx = Sin(3x)

Combine like terms: 8insx + -2insx = 6insx
6insx = Sin(3x)

Remove parenthesis around (3x)
6insx = inS * 3x

Reorder the terms for easier multiplication:
6insx = 3inS * x

Multiply inS * x
6insx = 3inxS

Solving
6insx = 3inxS

Solving for variable 'i'.

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

Add '-3inxS' to each side of the equation.
6insx + -3inxS = 3inxS + -3inxS

Combine like terms: 3inxS + -3inxS = 0
6insx + -3inxS = 0

Factor out the Greatest Common Factor (GCF), '3inx'.
3inx(2s + -1S) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'inx' equal to zero and attempt to solve: Simplifying inx = 0 Solving inx = 0 Move all terms containing i to the left, all other terms to the right. Simplifying inx = 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 '(2s + -1S)' equal to zero and attempt to solve: Simplifying 2s + -1S = 0 Reorder the terms: -1S + 2s = 0 Solving -1S + 2s = 0 Move all terms containing i to the left, all other terms to the right. Add 'S' to each side of the equation. -1S + S + 2s = 0 + S Combine like terms: -1S + S = 0 0 + 2s = 0 + S 2s = 0 + S Remove the zero: 2s = S Add '-2s' to each side of the equation. 2s + -2s = S + -2s Combine like terms: 2s + -2s = 0 0 = S + -2s Simplifying 0 = S + -2s 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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