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Simplifying cos(2x) = 6cos2(x) + -2 Remove parenthesis around (2x) cos * 2x = 6cos2(x) + -2 Reorder the terms for easier multiplication: 2cos * x = 6cos2(x) + -2 Multiply cos * x 2cosx = 6cos2(x) + -2 Multiply cos2 * x 2cosx = 6cos2x + -2 Reorder the terms: 2cosx = -2 + 6cos2x Solving 2cosx = -2 + 6cos2x Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-6cos2x' to each side of the equation. 2cosx + -6cos2x = -2 + 6cos2x + -6cos2x Combine like terms: 6cos2x + -6cos2x = 0 2cosx + -6cos2x = -2 + 0 2cosx + -6cos2x = -2 Reorder the terms: 2 + 2cosx + -6cos2x = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 2cosx + -6cos2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + cosx + -3cos2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + cosx + -3cos2x)' equal to zero and attempt to solve: Simplifying 1 + cosx + -3cos2x = 0 Solving 1 + cosx + -3cos2x = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + cosx + -1 + -3cos2x = 0 + -1 Reorder the terms: 1 + -1 + cosx + -3cos2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + cosx + -3cos2x = 0 + -1 cosx + -3cos2x = 0 + -1 Combine like terms: 0 + -1 = -1 cosx + -3cos2x = -1 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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