cos^5(20)=c*cos^5(20)+cos^3(20)+cos(20)

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Solution for cos^5(20)=c*cos^5(20)+cos^3(20)+cos(20) equation: 


Simplifying
cos5(20) = c * cos5(20) + cos3(20) + cos(20)

Reorder the terms for easier multiplication:
20cos5 = c * cos5(20) + cos3(20) + cos(20)

Reorder the terms for easier multiplication:
20cos5 = 20c * cos5 + cos3(20) + cos(20)

Multiply c * cos5
20cos5 = 20c2os5 + cos3(20) + cos(20)

Reorder the terms for easier multiplication:
20cos5 = 20c2os5 + 20cos3 + cos(20)

Reorder the terms for easier multiplication:
20cos5 = 20c2os5 + 20cos3 + 20cos

Reorder the terms:
20cos5 = 20cos + 20cos3 + 20c2os5

Solving
20cos5 = 20cos + 20cos3 + 20c2os5

Solving for variable 'c'.

Reorder the terms:
-20cos + -20cos3 + 20cos5 + -20c2os5 = 20cos + 20cos3 + 20c2os5 + -20cos + -20cos3 + -20c2os5

Reorder the terms:
-20cos + -20cos3 + 20cos5 + -20c2os5 = 20cos + -20cos + 20cos3 + -20cos3 + 20c2os5 + -20c2os5

Combine like terms: 20cos + -20cos = 0
-20cos + -20cos3 + 20cos5 + -20c2os5 = 0 + 20cos3 + -20cos3 + 20c2os5 + -20c2os5
-20cos + -20cos3 + 20cos5 + -20c2os5 = 20cos3 + -20cos3 + 20c2os5 + -20c2os5

Combine like terms: 20cos3 + -20cos3 = 0
-20cos + -20cos3 + 20cos5 + -20c2os5 = 0 + 20c2os5 + -20c2os5
-20cos + -20cos3 + 20cos5 + -20c2os5 = 20c2os5 + -20c2os5

Combine like terms: 20c2os5 + -20c2os5 = 0
-20cos + -20cos3 + 20cos5 + -20c2os5 = 0

Factor out the Greatest Common Factor (GCF), '20cos'.
20cos(-1 + -1s2 + s4 + -1cs4) = 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 '(-1 + -1s2 + s4 + -1cs4)' equal to zero and attempt to solve:

Simplifying
-1 + -1s2 + s4 + -1cs4 = 0

Reorder the terms:
-1 + -1cs4 + -1s2 + s4 = 0

Solving
-1 + -1cs4 + -1s2 + s4 = 0

Move all terms containing c to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + -1cs4 + -1s2 + 1 + s4 = 0 + 1

Reorder the terms:
-1 + 1 + -1cs4 + -1s2 + s4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1cs4 + -1s2 + s4 = 0 + 1
-1cs4 + -1s2 + s4 = 0 + 1

Combine like terms: 0 + 1 = 1
-1cs4 + -1s2 + s4 = 1

Add 's2' to each side of the equation.
-1cs4 + -1s2 + s2 + s4 = 1 + s2

Combine like terms: -1s2 + s2 = 0
-1cs4 + 0 + s4 = 1 + s2
-1cs4 + s4 = 1 + s2

Add '-1s4' to each side of the equation.
-1cs4 + s4 + -1s4 = 1 + s2 + -1s4

Combine like terms: s4 + -1s4 = 0
-1cs4 + 0 = 1 + s2 + -1s4
-1cs4 = 1 + s2 + -1s4

Divide each side by '-1s4'.
c = -1s-4 + -1s-2 + 1

Simplifying
c = -1s-4 + -1s-2 + 1

Reorder the terms:
c = 1 + -1s-4 + -1s-2
Solution
c = {1 + -1s-4 + -1s-2}

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