Sin(8x)=8sin(x)cos(x)cos(2x)cos(4x)

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Solution for Sin(8x)=8sin(x)cos(x)cos(2x)cos(4x) equation: 


Simplifying
Sin(8x) = 8sin(x) * cos(x) * cos(2x) * cos(4x)

Remove parenthesis around (8x)
inS * 8x = 8sin(x) * cos(x) * cos(2x) * cos(4x)

Reorder the terms for easier multiplication:
8inS * x = 8sin(x) * cos(x) * cos(2x) * cos(4x)

Multiply inS * x
8inxS = 8sin(x) * cos(x) * cos(2x) * cos(4x)

Remove parenthesis around (2x)
8inxS = 8ins * x * cos * x * cos * 2x * cos(4x)

Remove parenthesis around (4x)
8inxS = 8ins * x * cos * x * cos * 2x * cos * 4x

Reorder the terms for easier multiplication:
8inxS = 8 * 2 * 4ins * x * cos * x * cos * x * cos * x

Multiply 8 * 2
8inxS = 16 * 4ins * x * cos * x * cos * x * cos * x

Multiply 16 * 4
8inxS = 64ins * x * cos * x * cos * x * cos * x

Multiply ins * x
8inxS = 64insx * cos * x * cos * x * cos * x

Multiply insx * cos
8inxS = 64cinos2x * x * cos * x * cos * x

Multiply cinos2x * x
8inxS = 64cinos2x2 * cos * x * cos * x

Multiply cinos2x2 * cos
8inxS = 64c2ino2s3x2 * x * cos * x

Multiply c2ino2s3x2 * x
8inxS = 64c2ino2s3x3 * cos * x

Multiply c2ino2s3x3 * cos
8inxS = 64c3ino3s4x3 * x

Multiply c3ino3s4x3 * x
8inxS = 64c3ino3s4x4

Solving
8inxS = 64c3ino3s4x4

Solving for variable 'i'.

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

Add '-64c3ino3s4x4' to each side of the equation.
-64c3ino3s4x4 + 8inxS = 64c3ino3s4x4 + -64c3ino3s4x4

Combine like terms: 64c3ino3s4x4 + -64c3ino3s4x4 = 0
-64c3ino3s4x4 + 8inxS = 0

Factor out the Greatest Common Factor (GCF), '8inx'.
8inx(-8c3o3s4x3 + S) = 0

Ignore the factor 8.

Subproblem 1
Set the factor 'inx' equal to zero and attempt to solve:

Simplifying
inx = 0

Solving
inx = 0

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

Simplifying
inx = 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 '(-8c3o3s4x3 + S)' equal to zero and attempt to solve:

Simplifying
-8c3o3s4x3 + S = 0

Reorder the terms:
S + -8c3o3s4x3 = 0

Solving
S + -8c3o3s4x3 = 0

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

Add '-1S' to each side of the equation.
S + -1S + -8c3o3s4x3 = 0 + -1S

Combine like terms: S + -1S = 0
0 + -8c3o3s4x3 = 0 + -1S
-8c3o3s4x3 = 0 + -1S
Remove the zero:
-8c3o3s4x3 = -1S

Add '8c3o3s4x3' to each side of the equation.
-8c3o3s4x3 + 8c3o3s4x3 = -1S + 8c3o3s4x3

Combine like terms: -8c3o3s4x3 + 8c3o3s4x3 = 0
0 = -1S + 8c3o3s4x3

Simplifying
0 = -1S + 8c3o3s4x3

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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