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Simplifying cos5(20) = a * cos5(20) + b * cos3(20) + c * cos(20) Reorder the terms for easier multiplication: 20cos5 = a * cos5(20) + b * cos3(20) + c * cos(20) Reorder the terms for easier multiplication: 20cos5 = 20a * cos5 + b * cos3(20) + c * cos(20) Multiply a * cos5 20cos5 = 20acos5 + b * cos3(20) + c * cos(20) Reorder the terms for easier multiplication: 20cos5 = 20acos5 + 20b * cos3 + c * cos(20) Multiply b * cos3 20cos5 = 20acos5 + 20bcos3 + c * cos(20) Reorder the terms for easier multiplication: 20cos5 = 20acos5 + 20bcos3 + 20c * cos Multiply c * cos 20cos5 = 20acos5 + 20bcos3 + 20c2os Solving 20cos5 = 20acos5 + 20bcos3 + 20c2os Solving for variable 'c'. Reorder the terms: -20acos5 + -20bcos3 + 20cos5 + -20c2os = 20acos5 + 20bcos3 + 20c2os + -20acos5 + -20bcos3 + -20c2os Reorder the terms: -20acos5 + -20bcos3 + 20cos5 + -20c2os = 20acos5 + -20acos5 + 20bcos3 + -20bcos3 + 20c2os + -20c2os Combine like terms: 20acos5 + -20acos5 = 0 -20acos5 + -20bcos3 + 20cos5 + -20c2os = 0 + 20bcos3 + -20bcos3 + 20c2os + -20c2os -20acos5 + -20bcos3 + 20cos5 + -20c2os = 20bcos3 + -20bcos3 + 20c2os + -20c2os Combine like terms: 20bcos3 + -20bcos3 = 0 -20acos5 + -20bcos3 + 20cos5 + -20c2os = 0 + 20c2os + -20c2os -20acos5 + -20bcos3 + 20cos5 + -20c2os = 20c2os + -20c2os Combine like terms: 20c2os + -20c2os = 0 -20acos5 + -20bcos3 + 20cos5 + -20c2os = 0 Factor out the Greatest Common Factor (GCF), '20cos'. 20cos(-1as4 + -1bs2 + s4 + -1c) = 0 Ignore the factor 20.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 '(-1as4 + -1bs2 + s4 + -1c)' equal to zero and attempt to solve: Simplifying -1as4 + -1bs2 + s4 + -1c = 0 Reorder the terms: -1as4 + -1bs2 + -1c + s4 = 0 Solving -1as4 + -1bs2 + -1c + s4 = 0 Move all terms containing c to the left, all other terms to the right. Add 'as4' to each side of the equation. -1as4 + -1bs2 + -1c + as4 + s4 = 0 + as4 Reorder the terms: -1as4 + as4 + -1bs2 + -1c + s4 = 0 + as4 Combine like terms: -1as4 + as4 = 0 0 + -1bs2 + -1c + s4 = 0 + as4 -1bs2 + -1c + s4 = 0 + as4 Remove the zero: -1bs2 + -1c + s4 = as4 Add 'bs2' to each side of the equation. -1bs2 + -1c + bs2 + s4 = as4 + bs2 Reorder the terms: -1bs2 + bs2 + -1c + s4 = as4 + bs2 Combine like terms: -1bs2 + bs2 = 0 0 + -1c + s4 = as4 + bs2 -1c + s4 = as4 + bs2 Add '-1s4' to each side of the equation. -1c + s4 + -1s4 = as4 + bs2 + -1s4 Combine like terms: s4 + -1s4 = 0 -1c + 0 = as4 + bs2 + -1s4 -1c = as4 + bs2 + -1s4 Divide each side by '-1'. c = -1as4 + -1bs2 + s4 Simplifying c = -1as4 + -1bs2 + s4Solution
c = {-1as4 + -1bs2 + s4}
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