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Simplifying 4cos(2x + 30) + 1 = 1 Reorder the terms: 4cos(30 + 2x) + 1 = 1 (30 * 4cos + 2x * 4cos) + 1 = 1 (120cos + 8cosx) + 1 = 1 Reorder the terms: 1 + 120cos + 8cosx = 1 Add '-1' to each side of the equation. 1 + 120cos + -1 + 8cosx = 1 + -1 Reorder the terms: 1 + -1 + 120cos + 8cosx = 1 + -1 Combine like terms: 1 + -1 = 0 0 + 120cos + 8cosx = 1 + -1 120cos + 8cosx = 1 + -1 Combine like terms: 1 + -1 = 0 120cos + 8cosx = 0 Solving 120cos + 8cosx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '8cos'. 8cos(15 + x) = 0 Ignore the factor 8.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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