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Simplifying cos(x + 30) = cos(60 + -1x) Reorder the terms: cos(30 + x) = cos(60 + -1x) (30 * cos + x * cos) = cos(60 + -1x) (30cos + cosx) = cos(60 + -1x) 30cos + cosx = (60 * cos + -1x * cos) 30cos + cosx = (60cos + -1cosx) Solving 30cos + cosx = 60cos + -1cosx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-60cos' to each side of the equation. 30cos + -60cos + cosx = 60cos + -60cos + -1cosx Combine like terms: 30cos + -60cos = -30cos -30cos + cosx = 60cos + -60cos + -1cosx Combine like terms: 60cos + -60cos = 0 -30cos + cosx = 0 + -1cosx -30cos + cosx = -1cosx Add 'cosx' to each side of the equation. -30cos + cosx + cosx = -1cosx + cosx Combine like terms: cosx + cosx = 2cosx -30cos + 2cosx = -1cosx + cosx Combine like terms: -1cosx + cosx = 0 -30cos + 2cosx = 0 Factor out the Greatest Common Factor (GCF), '2cos'. 2cos(-15 + x) = 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 '(-15 + x)' equal to zero and attempt to solve: Simplifying -15 + x = 0 Solving -15 + x = 0 Move all terms containing c to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + x = 0 + 15 x = 0 + 15 Combine like terms: 0 + 15 = 15 x = 15 Add '-1x' to each side of the equation. x + -1x = 15 + -1x Combine like terms: x + -1x = 0 0 = 15 + -1x Simplifying 0 = 15 + -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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