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Simplifying sin(8x) + sin(2x) = 2sin(5x) * cos(3x) Remove parenthesis around (8x) ins * 8x + sin(2x) = 2sin(5x) * cos(3x) Reorder the terms for easier multiplication: 8ins * x + sin(2x) = 2sin(5x) * cos(3x) Multiply ins * x 8insx + sin(2x) = 2sin(5x) * cos(3x) Remove parenthesis around (2x) 8insx + ins * 2x = 2sin(5x) * cos(3x) Reorder the terms for easier multiplication: 8insx + 2ins * x = 2sin(5x) * cos(3x) Multiply ins * x 8insx + 2insx = 2sin(5x) * cos(3x) Combine like terms: 8insx + 2insx = 10insx 10insx = 2sin(5x) * cos(3x) Remove parenthesis around (5x) 10insx = 2ins * 5x * cos(3x) Remove parenthesis around (3x) 10insx = 2ins * 5x * cos * 3x Reorder the terms for easier multiplication: 10insx = 2 * 5 * 3ins * x * cos * x Multiply 2 * 5 10insx = 10 * 3ins * x * cos * x Multiply 10 * 3 10insx = 30ins * x * cos * x Multiply ins * x 10insx = 30insx * cos * x Multiply insx * cos 10insx = 30cinos2x * x Multiply cinos2x * x 10insx = 30cinos2x2 Solving 10insx = 30cinos2x2 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-30cinos2x2' to each side of the equation. -30cinos2x2 + 10insx = 30cinos2x2 + -30cinos2x2 Combine like terms: 30cinos2x2 + -30cinos2x2 = 0 -30cinos2x2 + 10insx = 0 Factor out the Greatest Common Factor (GCF), '10insx'. 10insx(-3cosx + 1) = 0 Ignore the factor 10.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 '(-3cosx + 1)' equal to zero and attempt to solve: Simplifying -3cosx + 1 = 0 Reorder the terms: 1 + -3cosx = 0 Solving 1 + -3cosx = 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 + -3cosx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3cosx = 0 + -1 -3cosx = 0 + -1 Combine like terms: 0 + -1 = -1 -3cosx = -1 Add '3cosx' to each side of the equation. -3cosx + 3cosx = -1 + 3cosx Combine like terms: -3cosx + 3cosx = 0 0 = -1 + 3cosx Simplifying 0 = -1 + 3cosx 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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