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Simplifying cos(85 + x) = -1cos(5 + 3x) (85 * cos + x * cos) = -1cos(5 + 3x) (85cos + cosx) = -1cos(5 + 3x) 85cos + cosx = (5 * -1cos + 3x * -1cos) 85cos + cosx = (-5cos + -3cosx) Solving 85cos + cosx = -5cos + -3cosx 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. 85cos + 5cos + cosx = -5cos + 5cos + -3cosx Combine like terms: 85cos + 5cos = 90cos 90cos + cosx = -5cos + 5cos + -3cosx Combine like terms: -5cos + 5cos = 0 90cos + cosx = 0 + -3cosx 90cos + cosx = -3cosx Add '3cosx' to each side of the equation. 90cos + cosx + 3cosx = -3cosx + 3cosx Combine like terms: cosx + 3cosx = 4cosx 90cos + 4cosx = -3cosx + 3cosx Combine like terms: -3cosx + 3cosx = 0 90cos + 4cosx = 0 Factor out the Greatest Common Factor (GCF), '2cos'. 2cos(45 + 2x) = 0 Ignore the factor 2.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 '(45 + 2x)' equal to zero and attempt to solve: Simplifying 45 + 2x = 0 Solving 45 + 2x = 0 Move all terms containing c to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + 2x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 2x = 0 + -45 2x = 0 + -45 Combine like terms: 0 + -45 = -45 2x = -45 Add '-2x' to each side of the equation. 2x + -2x = -45 + -2x Combine like terms: 2x + -2x = 0 0 = -45 + -2x Simplifying 0 = -45 + -2x 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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