cos(7X)+cos(x)+cos(4x)=0

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Solution for cos(7X)+cos(x)+cos(4x)=0 equation: 


Simplifying
cos(7X) + cos(x) + cos(4x) = 0

Remove parenthesis around (7X)
cos * 7X + cos(x) + cos(4x) = 0

Reorder the terms for easier multiplication:
7cos * X + cos(x) + cos(4x) = 0

Multiply cos * X
7cosX + cos(x) + cos(4x) = 0

Multiply cos * x
7cosX + cosx + cos(4x) = 0

Remove parenthesis around (4x)
7cosX + cosx + cos * 4x = 0

Reorder the terms for easier multiplication:
7cosX + cosx + 4cos * x = 0

Multiply cos * x
7cosX + cosx + 4cosx = 0

Combine like terms: cosx + 4cosx = 5cosx
7cosX + 5cosx = 0

Solving
7cosX + 5cosx = 0

Solving for variable 'c'.

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

Factor out the Greatest Common Factor (GCF), 'cos'.
cos(7X + 5x) = 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 '(7X + 5x)' equal to zero and attempt to solve:

Simplifying
7X + 5x = 0

Solving
7X + 5x = 0

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

Add '-7X' to each side of the equation.
7X + -7X + 5x = 0 + -7X

Combine like terms: 7X + -7X = 0
0 + 5x = 0 + -7X
5x = 0 + -7X
Remove the zero:
5x = -7X

Add '-5x' to each side of the equation.
5x + -5x = -7X + -5x

Combine like terms: 5x + -5x = 0
0 = -7X + -5x

Simplifying
0 = -7X + -5x

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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