cos(5x)+cos(7x)=cos(n+6x)

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Solution for cos(5x)+cos(7x)=cos(n+6x) equation:


Simplifying
cos(5x) + cos(7x) = cos(n + 6x)

Remove parenthesis around (5x)
cos * 5x + cos(7x) = cos(n + 6x)

Reorder the terms for easier multiplication:
5cos * x + cos(7x) = cos(n + 6x)

Multiply cos * x
5cosx + cos(7x) = cos(n + 6x)

Remove parenthesis around (7x)
5cosx + cos * 7x = cos(n + 6x)

Reorder the terms for easier multiplication:
5cosx + 7cos * x = cos(n + 6x)

Multiply cos * x
5cosx + 7cosx = cos(n + 6x)

Combine like terms: 5cosx + 7cosx = 12cosx
12cosx = cos(n + 6x)
12cosx = (n * cos + 6x * cos)
12cosx = (cnos + 6cosx)

Solving
12cosx = cnos + 6cosx

Solving for variable 'c'.

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

Add '-1cnos' to each side of the equation.
-1cnos + 12cosx = cnos + -1cnos + 6cosx

Combine like terms: cnos + -1cnos = 0
-1cnos + 12cosx = 0 + 6cosx
-1cnos + 12cosx = 6cosx

Add '-6cosx' to each side of the equation.
-1cnos + 12cosx + -6cosx = 6cosx + -6cosx

Combine like terms: 12cosx + -6cosx = 6cosx
-1cnos + 6cosx = 6cosx + -6cosx

Combine like terms: 6cosx + -6cosx = 0
-1cnos + 6cosx = 0

Factor out the Greatest Common Factor (GCF), 'cos'.
cos(-1n + 6x) = 0

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 '(-1n + 6x)' equal to zero and attempt to solve: Simplifying -1n + 6x = 0 Solving -1n + 6x = 0 Move all terms containing c to the left, all other terms to the right. Add 'n' to each side of the equation. -1n + n + 6x = 0 + n Combine like terms: -1n + n = 0 0 + 6x = 0 + n 6x = 0 + n Remove the zero: 6x = n Add '-6x' to each side of the equation. 6x + -6x = n + -6x Combine like terms: 6x + -6x = 0 0 = n + -6x Simplifying 0 = n + -6x 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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