(sin^5x*cos^2x)=(cos^2x-2cos^4x+cos^6x)

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Solution for (sin^5x*cos^2x)=(cos^2x-2cos^4x+cos^6x) equation: 


Simplifying
(sin5x * cos2x) = (cos2x + -2cos4x + cos6x)

Multiply in5sx * cos2x
(cin5os3x2) = (cos2x + -2cos4x + cos6x)
cin5os3x2 = (cos2x + -2cos4x + cos6x)

Remove parenthesis around (cos2x + -2cos4x + cos6x)
cin5os3x2 = cos2x + -2cos4x + cos6x

Solving
cin5os3x2 = cos2x + -2cos4x + cos6x

Solving for variable 'c'.

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

Add '-1cos2x' to each side of the equation.
cin5os3x2 + -1cos2x = cos2x + -2cos4x + -1cos2x + cos6x

Reorder the terms:
cin5os3x2 + -1cos2x = cos2x + -1cos2x + -2cos4x + cos6x

Combine like terms: cos2x + -1cos2x = 0
cin5os3x2 + -1cos2x = 0 + -2cos4x + cos6x
cin5os3x2 + -1cos2x = -2cos4x + cos6x

Add '2cos4x' to each side of the equation.
cin5os3x2 + -1cos2x + 2cos4x = -2cos4x + 2cos4x + cos6x

Combine like terms: -2cos4x + 2cos4x = 0
cin5os3x2 + -1cos2x + 2cos4x = 0 + cos6x
cin5os3x2 + -1cos2x + 2cos4x = cos6x

Add '-1cos6x' to each side of the equation.
cin5os3x2 + -1cos2x + 2cos4x + -1cos6x = cos6x + -1cos6x

Combine like terms: cos6x + -1cos6x = 0
cin5os3x2 + -1cos2x + 2cos4x + -1cos6x = 0

Factor out the Greatest Common Factor (GCF), 'cos2x'.
cos2x(in5sx + -1 + 2s2 + -1s4) = 0


Subproblem 1
Set the factor 'cos2x' equal to zero and attempt to solve:

Simplifying
cos2x = 0

Solving
cos2x = 0

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

Simplifying
cos2x = 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 '(in5sx + -1 + 2s2 + -1s4)' equal to zero and attempt to solve:

Simplifying
in5sx + -1 + 2s2 + -1s4 = 0

Reorder the terms:
-1 + in5sx + 2s2 + -1s4 = 0

Solving
-1 + in5sx + 2s2 + -1s4 = 0

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

Add '1' to each side of the equation.
-1 + in5sx + 2s2 + 1 + -1s4 = 0 + 1

Reorder the terms:
-1 + 1 + in5sx + 2s2 + -1s4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + in5sx + 2s2 + -1s4 = 0 + 1
in5sx + 2s2 + -1s4 = 0 + 1

Combine like terms: 0 + 1 = 1
in5sx + 2s2 + -1s4 = 1

Add '-1in5sx' to each side of the equation.
in5sx + 2s2 + -1in5sx + -1s4 = 1 + -1in5sx

Reorder the terms:
in5sx + -1in5sx + 2s2 + -1s4 = 1 + -1in5sx

Combine like terms: in5sx + -1in5sx = 0
0 + 2s2 + -1s4 = 1 + -1in5sx
2s2 + -1s4 = 1 + -1in5sx

Add '-2s2' to each side of the equation.
2s2 + -2s2 + -1s4 = 1 + -1in5sx + -2s2

Combine like terms: 2s2 + -2s2 = 0
0 + -1s4 = 1 + -1in5sx + -2s2
-1s4 = 1 + -1in5sx + -2s2

Add 's4' to each side of the equation.
-1s4 + s4 = 1 + -1in5sx + -2s2 + s4

Combine like terms: -1s4 + s4 = 0
0 = 1 + -1in5sx + -2s2 + s4

Simplifying
0 = 1 + -1in5sx + -2s2 + s4

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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