sin(3x)=-sin^3(x)+3cos^2(x)

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Solution for sin(3x)=-sin^3(x)+3cos^2(x) equation:


Simplifying
sin(3x) = -1sin3(x) + 3cos2(x)

Remove parenthesis around (3x)
ins * 3x = -1sin3(x) + 3cos2(x)

Reorder the terms for easier multiplication:
3ins * x = -1sin3(x) + 3cos2(x)

Multiply ins * x
3insx = -1sin3(x) + 3cos2(x)

Multiply in3s * x
3insx = -1in3sx + 3cos2(x)

Multiply cos2 * x
3insx = -1in3sx + 3cos2x

Reorder the terms:
3insx = 3cos2x + -1in3sx

Solving
3insx = 3cos2x + -1in3sx

Solving for variable 'i'.

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

Add 'in3sx' to each side of the equation.
3insx + in3sx = 3cos2x + -1in3sx + in3sx

Combine like terms: -1in3sx + in3sx = 0
3insx + in3sx = 3cos2x + 0
3insx + in3sx = 3cos2x

Reorder the terms:
-3cos2x + 3insx + in3sx = 3cos2x + -3cos2x

Combine like terms: 3cos2x + -3cos2x = 0
-3cos2x + 3insx + in3sx = 0

Factor out the Greatest Common Factor (GCF), 'sx'.
sx(-3cos + 3in + in3) = 0

Subproblem 1

Set the factor 'sx' equal to zero and attempt to solve: Simplifying sx = 0 Solving sx = 0 Move all terms containing i to the left, all other terms to the right. Add '-1sx' to each side of the equation. sx + -1sx = 0 + -1sx Remove the zero: 0 = -1sx Simplifying 0 = -1sx 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 '(-3cos + 3in + in3)' equal to zero and attempt to solve: Simplifying -3cos + 3in + in3 = 0 Solving -3cos + 3in + in3 = 0 Move all terms containing i to the left, all other terms to the right. Add '3cos' to each side of the equation. -3cos + 3in + 3cos + in3 = 0 + 3cos Reorder the terms: -3cos + 3cos + 3in + in3 = 0 + 3cos Combine like terms: -3cos + 3cos = 0 0 + 3in + in3 = 0 + 3cos 3in + in3 = 0 + 3cos Remove the zero: 3in + in3 = 3cos 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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