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Simplifying cos(2x + 3) = -1cos(x + -5) Reorder the terms: cos(3 + 2x) = -1cos(x + -5) (3 * cos + 2x * cos) = -1cos(x + -5) (3cos + 2cosx) = -1cos(x + -5) Reorder the terms: 3cos + 2cosx = -1cos(-5 + x) 3cos + 2cosx = (-5 * -1cos + x * -1cos) 3cos + 2cosx = (5cos + -1cosx) Solving 3cos + 2cosx = 5cos + -1cosx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5cos' to each side of the equation. 3cos + -5cos + 2cosx = 5cos + -5cos + -1cosx Combine like terms: 3cos + -5cos = -2cos -2cos + 2cosx = 5cos + -5cos + -1cosx Combine like terms: 5cos + -5cos = 0 -2cos + 2cosx = 0 + -1cosx -2cos + 2cosx = -1cosx Add 'cosx' to each side of the equation. -2cos + 2cosx + cosx = -1cosx + cosx Combine like terms: 2cosx + cosx = 3cosx -2cos + 3cosx = -1cosx + cosx Combine like terms: -1cosx + cosx = 0 -2cos + 3cosx = 0 Factor out the Greatest Common Factor (GCF), 'cos'. cos(-2 + 3x) = 0Subproblem 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 '(-2 + 3x)' equal to zero and attempt to solve: Simplifying -2 + 3x = 0 Solving -2 + 3x = 0 Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x = 0 + 2 3x = 0 + 2 Combine like terms: 0 + 2 = 2 3x = 2 Add '-3x' to each side of the equation. 3x + -3x = 2 + -3x Combine like terms: 3x + -3x = 0 0 = 2 + -3x Simplifying 0 = 2 + -3x 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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