2-cos(2x)-2cos(4x)+cos(6x)=32cos^2(x)sin^4(x)

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Solution for 2-cos(2x)-2cos(4x)+cos(6x)=32cos^2(x)sin^4(x) equation: 


Simplifying
2 + -1cos(2x) + -2cos(4x) + cos(6x) = 32cos2(x) * sin4(x)

Remove parenthesis around (2x)
2 + -1cos * 2x + -2cos(4x) + cos(6x) = 32cos2(x) * sin4(x)

Reorder the terms for easier multiplication:
2 + -1 * 2cos * x + -2cos(4x) + cos(6x) = 32cos2(x) * sin4(x)

Multiply -1 * 2
2 + -2cos * x + -2cos(4x) + cos(6x) = 32cos2(x) * sin4(x)

Multiply cos * x
2 + -2cosx + -2cos(4x) + cos(6x) = 32cos2(x) * sin4(x)

Remove parenthesis around (4x)
2 + -2cosx + -2cos * 4x + cos(6x) = 32cos2(x) * sin4(x)

Reorder the terms for easier multiplication:
2 + -2cosx + -2 * 4cos * x + cos(6x) = 32cos2(x) * sin4(x)

Multiply -2 * 4
2 + -2cosx + -8cos * x + cos(6x) = 32cos2(x) * sin4(x)

Multiply cos * x
2 + -2cosx + -8cosx + cos(6x) = 32cos2(x) * sin4(x)

Remove parenthesis around (6x)
2 + -2cosx + -8cosx + cos * 6x = 32cos2(x) * sin4(x)

Reorder the terms for easier multiplication:
2 + -2cosx + -8cosx + 6cos * x = 32cos2(x) * sin4(x)

Multiply cos * x
2 + -2cosx + -8cosx + 6cosx = 32cos2(x) * sin4(x)

Combine like terms: -2cosx + -8cosx = -10cosx
2 + -10cosx + 6cosx = 32cos2(x) * sin4(x)

Combine like terms: -10cosx + 6cosx = -4cosx
2 + -4cosx = 32cos2(x) * sin4(x)

Multiply cos2 * x
2 + -4cosx = 32cos2x * in4s * x

Multiply cos2x * in4s
2 + -4cosx = 32cin4os3x * x

Multiply cin4os3x * x
2 + -4cosx = 32cin4os3x2

Solving
2 + -4cosx = 32cin4os3x2

Solving for variable 'c'.

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

Add '-32cin4os3x2' to each side of the equation.
2 + -32cin4os3x2 + -4cosx = 32cin4os3x2 + -32cin4os3x2

Combine like terms: 32cin4os3x2 + -32cin4os3x2 = 0
2 + -32cin4os3x2 + -4cosx = 0

Add '-2' to each side of the equation.
2 + -32cin4os3x2 + -2 + -4cosx = 0 + -2

Reorder the terms:
2 + -2 + -32cin4os3x2 + -4cosx = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -32cin4os3x2 + -4cosx = 0 + -2
-32cin4os3x2 + -4cosx = 0 + -2

Combine like terms: 0 + -2 = -2
-32cin4os3x2 + -4cosx = -2

Reorder the terms:
2 + -32cin4os3x2 + -4cosx = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -32cin4os3x2 + -4cosx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -16cin4os3x2 + -2cosx) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -16cin4os3x2 + -2cosx)' equal to zero and attempt to solve:

Simplifying
1 + -16cin4os3x2 + -2cosx = 0

Solving
1 + -16cin4os3x2 + -2cosx = 0

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

Add '-1' to each side of the equation.
1 + -16cin4os3x2 + -1 + -2cosx = 0 + -1

Reorder the terms:
1 + -1 + -16cin4os3x2 + -2cosx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -16cin4os3x2 + -2cosx = 0 + -1
-16cin4os3x2 + -2cosx = 0 + -1

Combine like terms: 0 + -1 = -1
-16cin4os3x2 + -2cosx = -1

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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