5cos(2x)=5cos^2(x)-5sin^2(x)

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Solution for 5cos(2x)=5cos^2(x)-5sin^2(x) equation:


Simplifying
5cos(2x) = 5cos2(x) + -5sin2(x)

Remove parenthesis around (2x)
5cos * 2x = 5cos2(x) + -5sin2(x)

Reorder the terms for easier multiplication:
5 * 2cos * x = 5cos2(x) + -5sin2(x)

Multiply 5 * 2
10cos * x = 5cos2(x) + -5sin2(x)

Multiply cos * x
10cosx = 5cos2(x) + -5sin2(x)

Multiply cos2 * x
10cosx = 5cos2x + -5sin2(x)

Multiply in2s * x
10cosx = 5cos2x + -5in2sx

Solving
10cosx = 5cos2x + -5in2sx

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.
10cosx + -5cos2x = 5cos2x + -5cos2x + -5in2sx

Combine like terms: 5cos2x + -5cos2x = 0
10cosx + -5cos2x = 0 + -5in2sx
10cosx + -5cos2x = -5in2sx

Combine like terms: -5in2sx + 5in2sx = 0
10cosx + -5cos2x + 5in2sx = 0

Factor out the Greatest Common Factor (GCF), '5sx'.
5sx(2co + -1cos + in2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'sx' equal to zero and attempt to solve: Simplifying sx = 0 Solving sx = 0 Move all terms containing c to the left, all other terms to the right. Add '-1sx' to each side of the equation. sx + -1sx = 0 + -1sx Remove the zero: 0 = -1sx Simplifying 0 = -1sx 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 '(2co + -1cos + in2)' equal to zero and attempt to solve: Simplifying 2co + -1cos + in2 = 0 Solving 2co + -1cos + in2 = 0 Move all terms containing c to the left, all other terms to the right. Add '-1in2' to each side of the equation. 2co + -1cos + in2 + -1in2 = 0 + -1in2 Combine like terms: in2 + -1in2 = 0 2co + -1cos + 0 = 0 + -1in2 2co + -1cos = 0 + -1in2 Remove the zero: 2co + -1cos = -1in2 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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