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

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


Simplifying
sin5x * cos2x = (cos2x + -2os4x + cos6) * sinx

Multiply in5sx * cos2x
cin5os3x2 = (cos2x + -2os4x + cos6) * sinx

Reorder the terms:
cin5os3x2 = (cos2x + cos6 + -2os4x) * sinx

Reorder the terms for easier multiplication:
cin5os3x2 = insx(cos2x + cos6 + -2os4x)
cin5os3x2 = (cos2x * insx + cos6 * insx + -2os4x * insx)
cin5os3x2 = (cinos3x2 + cinos7x + -2inos5x2)

Solving
cin5os3x2 = cinos3x2 + cinos7x + -2inos5x2

Solving for variable 'c'.

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

Add '-1cinos3x2' to each side of the equation.
-1cinos3x2 + cin5os3x2 = cinos3x2 + cinos7x + -1cinos3x2 + -2inos5x2

Reorder the terms:
-1cinos3x2 + cin5os3x2 = cinos3x2 + -1cinos3x2 + cinos7x + -2inos5x2

Combine like terms: cinos3x2 + -1cinos3x2 = 0
-1cinos3x2 + cin5os3x2 = 0 + cinos7x + -2inos5x2
-1cinos3x2 + cin5os3x2 = cinos7x + -2inos5x2

Add '-1cinos7x' to each side of the equation.
-1cinos3x2 + -1cinos7x + cin5os3x2 = cinos7x + -1cinos7x + -2inos5x2

Combine like terms: cinos7x + -1cinos7x = 0
-1cinos3x2 + -1cinos7x + cin5os3x2 = 0 + -2inos5x2
-1cinos3x2 + -1cinos7x + cin5os3x2 = -2inos5x2

Combine like terms: -2inos5x2 + 2inos5x2 = 0
-1cinos3x2 + -1cinos7x + cin5os3x2 + 2inos5x2 = 0

Factor out the Greatest Common Factor (GCF), 'inos3x'.
inos3x(-1cx + -1cs4 + cn4x + 2s2x) = 0


Subproblem 1
Set the factor 'inos3x' equal to zero and attempt to solve:

Simplifying
inos3x = 0

Solving
inos3x = 0

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

Add '-1inos3x' to each side of the equation.
inos3x + -1inos3x = 0 + -1inos3x
Remove the zero:
0 = -1inos3x

Simplifying
0 = -1inos3x

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 '(-1cx + -1cs4 + cn4x + 2s2x)' equal to zero and attempt to solve:

Simplifying
-1cx + -1cs4 + cn4x + 2s2x = 0

Reorder the terms:
cn4x + -1cs4 + -1cx + 2s2x = 0

Solving
cn4x + -1cs4 + -1cx + 2s2x = 0

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

Add '-2s2x' to each side of the equation.
cn4x + -1cs4 + -1cx + 2s2x + -2s2x = 0 + -2s2x

Combine like terms: 2s2x + -2s2x = 0
cn4x + -1cs4 + -1cx + 0 = 0 + -2s2x
cn4x + -1cs4 + -1cx = 0 + -2s2x
Remove the zero:
cn4x + -1cs4 + -1cx = -2s2x

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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