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Simplifying sin(3x) = sinx(4cos + -1) Remove parenthesis around (3x) ins * 3x = sinx(4cos + -1) Reorder the terms for easier multiplication: 3ins * x = sinx(4cos + -1) Multiply ins * x 3insx = sinx(4cos + -1) Reorder the terms: 3insx = insx(-1 + 4cos) 3insx = (-1 * insx + 4cos * insx) Reorder the terms: 3insx = (4cinos2x + -1insx) 3insx = (4cinos2x + -1insx) Solving 3insx = 4cinos2x + -1insx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4cinos2x' to each side of the equation. -4cinos2x + 3insx = 4cinos2x + -4cinos2x + -1insx Combine like terms: 4cinos2x + -4cinos2x = 0 -4cinos2x + 3insx = 0 + -1insx -4cinos2x + 3insx = -1insx Add 'insx' to each side of the equation. -4cinos2x + 3insx + insx = -1insx + insx Combine like terms: 3insx + insx = 4insx -4cinos2x + 4insx = -1insx + insx Combine like terms: -1insx + insx = 0 -4cinos2x + 4insx = 0 Factor out the Greatest Common Factor (GCF), '4insx'. 4insx(-1cos + 1) = 0 Ignore the factor 4.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 '(-1cos + 1)' equal to zero and attempt to solve: Simplifying -1cos + 1 = 0 Reorder the terms: 1 + -1cos = 0 Solving 1 + -1cos = 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 + -1cos = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1cos = 0 + -1 -1cos = 0 + -1 Combine like terms: 0 + -1 = -1 -1cos = -1 Add 'cos' to each side of the equation. -1cos + cos = -1 + cos Combine like terms: -1cos + cos = 0 0 = -1 + cos Simplifying 0 = -1 + cos 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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