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Simplifying cos(20 + -1x) = cos(3x + 40) (20 * cos + -1x * cos) = cos(3x + 40) (20cos + -1cosx) = cos(3x + 40) Reorder the terms: 20cos + -1cosx = cos(40 + 3x) 20cos + -1cosx = (40 * cos + 3x * cos) 20cos + -1cosx = (40cos + 3cosx) Solving 20cos + -1cosx = 40cos + 3cosx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-40cos' to each side of the equation. 20cos + -40cos + -1cosx = 40cos + -40cos + 3cosx Combine like terms: 20cos + -40cos = -20cos -20cos + -1cosx = 40cos + -40cos + 3cosx Combine like terms: 40cos + -40cos = 0 -20cos + -1cosx = 0 + 3cosx -20cos + -1cosx = 3cosx Add '-3cosx' to each side of the equation. -20cos + -1cosx + -3cosx = 3cosx + -3cosx Combine like terms: -1cosx + -3cosx = -4cosx -20cos + -4cosx = 3cosx + -3cosx Combine like terms: 3cosx + -3cosx = 0 -20cos + -4cosx = 0 Factor out the Greatest Common Factor (GCF), '-4cos'. -4cos(5 + x) = 0 Ignore the factor -4.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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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