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Simplifying cos(3x) + cos(5x) + cos(7x) = cos(5x)(2cos(2x) + 1) Remove parenthesis around (3x) cos * 3x + cos(5x) + cos(7x) = cos(5x)(2cos(2x) + 1) Reorder the terms for easier multiplication: 3cos * x + cos(5x) + cos(7x) = cos(5x)(2cos(2x) + 1) Multiply cos * x 3cosx + cos(5x) + cos(7x) = cos(5x)(2cos(2x) + 1) Remove parenthesis around (5x) 3cosx + cos * 5x + cos(7x) = cos(5x)(2cos(2x) + 1) Reorder the terms for easier multiplication: 3cosx + 5cos * x + cos(7x) = cos(5x)(2cos(2x) + 1) Multiply cos * x 3cosx + 5cosx + cos(7x) = cos(5x)(2cos(2x) + 1) Remove parenthesis around (7x) 3cosx + 5cosx + cos * 7x = cos(5x)(2cos(2x) + 1) Reorder the terms for easier multiplication: 3cosx + 5cosx + 7cos * x = cos(5x)(2cos(2x) + 1) Multiply cos * x 3cosx + 5cosx + 7cosx = cos(5x)(2cos(2x) + 1) Combine like terms: 3cosx + 5cosx = 8cosx 8cosx + 7cosx = cos(5x)(2cos(2x) + 1) Combine like terms: 8cosx + 7cosx = 15cosx 15cosx = cos(5x)(2cos(2x) + 1) Remove parenthesis around (5x) 15cosx = cos * 5x(2cos(2x) + 1) Remove parenthesis around (2x) 15cosx = cos * 5x(2cos * 2x + 1) Reorder the terms for easier multiplication: 15cosx = cos * 5x(2 * 2cos * x + 1) Multiply 2 * 2 15cosx = cos * 5x(4cos * x + 1) Multiply cos * x 15cosx = cos * 5x(4cosx + 1) Reorder the terms: 15cosx = cos * 5x(1 + 4cosx) Reorder the terms for easier multiplication: 15cosx = 5cos * x(1 + 4cosx) Multiply cos * x 15cosx = 5cosx(1 + 4cosx) 15cosx = (1 * 5cosx + 4cosx * 5cosx) 15cosx = (5cosx + 20c2o2s2x2) Solving 15cosx = 5cosx + 20c2o2s2x2 Solving for variable 'c'. Combine like terms: 15cosx + -5cosx = 10cosx 10cosx + -20c2o2s2x2 = 5cosx + 20c2o2s2x2 + -5cosx + -20c2o2s2x2 Reorder the terms: 10cosx + -20c2o2s2x2 = 5cosx + -5cosx + 20c2o2s2x2 + -20c2o2s2x2 Combine like terms: 5cosx + -5cosx = 0 10cosx + -20c2o2s2x2 = 0 + 20c2o2s2x2 + -20c2o2s2x2 10cosx + -20c2o2s2x2 = 20c2o2s2x2 + -20c2o2s2x2 Combine like terms: 20c2o2s2x2 + -20c2o2s2x2 = 0 10cosx + -20c2o2s2x2 = 0 Factor out the Greatest Common Factor (GCF), '10cosx'. 10cosx(1 + -2cosx) = 0 Ignore the factor 10.Subproblem 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 '(1 + -2cosx)' equal to zero and attempt to solve: Simplifying 1 + -2cosx = 0 Solving 1 + -2cosx = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2cosx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2cosx = 0 + -1 -2cosx = 0 + -1 Combine like terms: 0 + -1 = -1 -2cosx = -1 Divide each side by '-2osx'. c = 0.5o-1s-1x-1 Simplifying c = 0.5o-1s-1x-1Solution
c = {0.5o-1s-1x-1}
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