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Simplifying cos5(x) = cos(x) + cos(2x) + cos(3x) + cos(4x) + cos(5x) Multiply cos5 * x cos5x = cos(x) + cos(2x) + cos(3x) + cos(4x) + cos(5x) Multiply cos * x cos5x = cosx + cos(2x) + cos(3x) + cos(4x) + cos(5x) Remove parenthesis around (2x) cos5x = cosx + cos * 2x + cos(3x) + cos(4x) + cos(5x) Reorder the terms for easier multiplication: cos5x = cosx + 2cos * x + cos(3x) + cos(4x) + cos(5x) Multiply cos * x cos5x = cosx + 2cosx + cos(3x) + cos(4x) + cos(5x) Remove parenthesis around (3x) cos5x = cosx + 2cosx + cos * 3x + cos(4x) + cos(5x) Reorder the terms for easier multiplication: cos5x = cosx + 2cosx + 3cos * x + cos(4x) + cos(5x) Multiply cos * x cos5x = cosx + 2cosx + 3cosx + cos(4x) + cos(5x) Remove parenthesis around (4x) cos5x = cosx + 2cosx + 3cosx + cos * 4x + cos(5x) Reorder the terms for easier multiplication: cos5x = cosx + 2cosx + 3cosx + 4cos * x + cos(5x) Multiply cos * x cos5x = cosx + 2cosx + 3cosx + 4cosx + cos(5x) Remove parenthesis around (5x) cos5x = cosx + 2cosx + 3cosx + 4cosx + cos * 5x Reorder the terms for easier multiplication: cos5x = cosx + 2cosx + 3cosx + 4cosx + 5cos * x Multiply cos * x cos5x = cosx + 2cosx + 3cosx + 4cosx + 5cosx Combine like terms: cosx + 2cosx = 3cosx cos5x = 3cosx + 3cosx + 4cosx + 5cosx Combine like terms: 3cosx + 3cosx = 6cosx cos5x = 6cosx + 4cosx + 5cosx Combine like terms: 6cosx + 4cosx = 10cosx cos5x = 10cosx + 5cosx Combine like terms: 10cosx + 5cosx = 15cosx cos5x = 15cosx Solving cos5x = 15cosx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-15cosx' to each side of the equation. -15cosx + cos5x = 15cosx + -15cosx Combine like terms: 15cosx + -15cosx = 0 -15cosx + cos5x = 0 Factor out the Greatest Common Factor (GCF), 'cosx'. cosx(-15 + s4) = 0Subproblem 1
Set the factor 'cosx' equal to zero and attempt to solve: Simplifying cosx = 0 Solving cosx = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cosx = 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 '(-15 + s4)' equal to zero and attempt to solve: Simplifying -15 + s4 = 0 Solving -15 + s4 = 0 Move all terms containing c to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + s4 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + s4 = 0 + 15 s4 = 0 + 15 Combine like terms: 0 + 15 = 15 s4 = 15 Add '-1s4' to each side of the equation. s4 + -1s4 = 15 + -1s4 Combine like terms: s4 + -1s4 = 0 0 = 15 + -1s4 Simplifying 0 = 15 + -1s4 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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