4cos^3(x)=cos(3x)+3cos(x)

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Solution for 4cos^3(x)=cos(3x)+3cos(x) equation: 


Simplifying
4cos3(x) = cos(3x) + 3cos(x)

Multiply cos3 * x
4cos3x = cos(3x) + 3cos(x)

Remove parenthesis around (3x)
4cos3x = cos * 3x + 3cos(x)

Reorder the terms for easier multiplication:
4cos3x = 3cos * x + 3cos(x)

Multiply cos * x
4cos3x = 3cosx + 3cos(x)

Multiply cos * x
4cos3x = 3cosx + 3cosx

Combine like terms: 3cosx + 3cosx = 6cosx
4cos3x = 6cosx

Solving
4cos3x = 6cosx

Solving for variable 'c'.

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

Add '-6cosx' to each side of the equation.
-6cosx + 4cos3x = 6cosx + -6cosx

Combine like terms: 6cosx + -6cosx = 0
-6cosx + 4cos3x = 0

Factor out the Greatest Common Factor (GCF), '2cosx'.
2cosx(-3 + 2s2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'cosx' equal to zero and attempt to solve:

Simplifying
cosx = 0

Solving
cosx = 0

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

Simplifying
cosx = 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 '(-3 + 2s2)' equal to zero and attempt to solve:

Simplifying
-3 + 2s2 = 0

Solving
-3 + 2s2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2s2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2s2 = 0 + 3
2s2 = 0 + 3

Combine like terms: 0 + 3 = 3
2s2 = 3

Add '-2s2' to each side of the equation.
2s2 + -2s2 = 3 + -2s2

Combine like terms: 2s2 + -2s2 = 0
0 = 3 + -2s2

Simplifying
0 = 3 + -2s2

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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