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Simplifying 5cos4x + -5sin4x = 5(cos2x + 2) Reorder the terms: 5cos4x + -5in4sx = 5(2 + cos2x) 5cos4x + -5in4sx = (2 * 5 + cos2x * 5) 5cos4x + -5in4sx = (10 + 5cos2x) Solving 5cos4x + -5in4sx = 10 + 5cos2x Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5cos2x' to each side of the equation. 5cos4x + -5cos2x + -5in4sx = 10 + 5cos2x + -5cos2x Reorder the terms: -5cos2x + 5cos4x + -5in4sx = 10 + 5cos2x + -5cos2x Combine like terms: 5cos2x + -5cos2x = 0 -5cos2x + 5cos4x + -5in4sx = 10 + 0 -5cos2x + 5cos4x + -5in4sx = 10 Add '5in4sx' to each side of the equation. -5cos2x + 5cos4x + -5in4sx + 5in4sx = 10 + 5in4sx Combine like terms: -5in4sx + 5in4sx = 0 -5cos2x + 5cos4x + 0 = 10 + 5in4sx -5cos2x + 5cos4x = 10 + 5in4sx Reorder the terms: -10 + -5cos2x + 5cos4x + -5in4sx = 10 + 5in4sx + -10 + -5in4sx Reorder the terms: -10 + -5cos2x + 5cos4x + -5in4sx = 10 + -10 + 5in4sx + -5in4sx Combine like terms: 10 + -10 = 0 -10 + -5cos2x + 5cos4x + -5in4sx = 0 + 5in4sx + -5in4sx -10 + -5cos2x + 5cos4x + -5in4sx = 5in4sx + -5in4sx Combine like terms: 5in4sx + -5in4sx = 0 -10 + -5cos2x + 5cos4x + -5in4sx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + -1cos2x + cos4x + -1in4sx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1cos2x + cos4x + -1in4sx)' equal to zero and attempt to solve: Simplifying -2 + -1cos2x + cos4x + -1in4sx = 0 Solving -2 + -1cos2x + cos4x + -1in4sx = 0 Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -1cos2x + cos4x + 2 + -1in4sx = 0 + 2 Reorder the terms: -2 + 2 + -1cos2x + cos4x + -1in4sx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1cos2x + cos4x + -1in4sx = 0 + 2 -1cos2x + cos4x + -1in4sx = 0 + 2 Combine like terms: 0 + 2 = 2 -1cos2x + cos4x + -1in4sx = 2 Add 'in4sx' to each side of the equation. -1cos2x + cos4x + -1in4sx + in4sx = 2 + in4sx Combine like terms: -1in4sx + in4sx = 0 -1cos2x + cos4x + 0 = 2 + in4sx -1cos2x + cos4x = 2 + in4sx 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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