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Simplifying cos(2x + 20) = -1cos(x + -11) Reorder the terms: cos(20 + 2x) = -1cos(x + -11) (20 * cos + 2x * cos) = -1cos(x + -11) (20cos + 2cosx) = -1cos(x + -11) Reorder the terms: 20cos + 2cosx = -1cos(-11 + x) 20cos + 2cosx = (-11 * -1cos + x * -1cos) 20cos + 2cosx = (11cos + -1cosx) Solving 20cos + 2cosx = 11cos + -1cosx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-11cos' to each side of the equation. 20cos + -11cos + 2cosx = 11cos + -11cos + -1cosx Combine like terms: 20cos + -11cos = 9cos 9cos + 2cosx = 11cos + -11cos + -1cosx Combine like terms: 11cos + -11cos = 0 9cos + 2cosx = 0 + -1cosx 9cos + 2cosx = -1cosx Add 'cosx' to each side of the equation. 9cos + 2cosx + cosx = -1cosx + cosx Combine like terms: 2cosx + cosx = 3cosx 9cos + 3cosx = -1cosx + cosx Combine like terms: -1cosx + cosx = 0 9cos + 3cosx = 0 Factor out the Greatest Common Factor (GCF), '3cos'. 3cos(3 + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'cos' equal to zero and attempt to solve: Simplifying cos = 0 Solving cos = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cos = 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x 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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