5*cos^3(x)=5*cos(x)

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Solution for 5*cos^3(x)=5*cos(x) equation:


Simplifying
5cos3(x) = 5cos(x)

Multiply cos3 * x
5cos3x = 5cos(x)

Multiply cos * x
5cos3x = 5cosx

Solving
5cos3x = 5cosx

Solving for variable 'c'.

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

Add '-5cosx' to each side of the equation.
-5cosx + 5cos3x = 5cosx + -5cosx

Combine like terms: 5cosx + -5cosx = 0
-5cosx + 5cos3x = 0

Factor out the Greatest Common Factor (GCF), '5cosx'.
5cosx(-1 + s2) = 0

Factor a difference between two squares.
5cosx((1 + s)(-1 + s)) = 0

Ignore the factor 5.

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 '(1 + s)' equal to zero and attempt to solve: Simplifying 1 + s = 0 Solving 1 + s = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + s = 0 + -1 s = 0 + -1 Combine like terms: 0 + -1 = -1 s = -1 Add '-1s' to each side of the equation. s + -1s = -1 + -1s Combine like terms: s + -1s = 0 0 = -1 + -1s Simplifying 0 = -1 + -1s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(-1 + s)' equal to zero and attempt to solve: Simplifying -1 + s = 0 Solving -1 + s = 0 Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = 0 + 1 Combine like terms: -1 + 1 = 0 0 + s = 0 + 1 s = 0 + 1 Combine like terms: 0 + 1 = 1 s = 1 Add '-1s' to each side of the equation. s + -1s = 1 + -1s Combine like terms: s + -1s = 0 0 = 1 + -1s Simplifying 0 = 1 + -1s 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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