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

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


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

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

Reorder the terms for easier multiplication:
cin5os3x2 = insx(cos2x + -2cos4x + cos6x)
cin5os3x2 = (cos2x * insx + -2cos4x * insx + cos6x * insx)
cin5os3x2 = (cinos3x2 + -2cinos5x2 + cinos7x2)

Solving
cin5os3x2 = cinos3x2 + -2cinos5x2 + cinos7x2

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 + -2cinos5x2 + -1cinos3x2 + cinos7x2

Reorder the terms:
-1cinos3x2 + cin5os3x2 = cinos3x2 + -1cinos3x2 + -2cinos5x2 + cinos7x2

Combine like terms: cinos3x2 + -1cinos3x2 = 0
-1cinos3x2 + cin5os3x2 = 0 + -2cinos5x2 + cinos7x2
-1cinos3x2 + cin5os3x2 = -2cinos5x2 + cinos7x2

Add '2cinos5x2' to each side of the equation.
-1cinos3x2 + 2cinos5x2 + cin5os3x2 = -2cinos5x2 + 2cinos5x2 + cinos7x2

Combine like terms: -2cinos5x2 + 2cinos5x2 = 0
-1cinos3x2 + 2cinos5x2 + cin5os3x2 = 0 + cinos7x2
-1cinos3x2 + 2cinos5x2 + cin5os3x2 = cinos7x2

Add '-1cinos7x2' to each side of the equation.
-1cinos3x2 + 2cinos5x2 + -1cinos7x2 + cin5os3x2 = cinos7x2 + -1cinos7x2

Combine like terms: cinos7x2 + -1cinos7x2 = 0
-1cinos3x2 + 2cinos5x2 + -1cinos7x2 + cin5os3x2 = 0

Factor out the Greatest Common Factor (GCF), 'cinos3x2'.
cinos3x2(-1 + 2s2 + -1s4 + n4) = 0

Subproblem 1

Set the factor 'cinos3x2' equal to zero and attempt to solve: Simplifying cinos3x2 = 0 Solving cinos3x2 = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cinos3x2 = 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 '(-1 + 2s2 + -1s4 + n4)' equal to zero and attempt to solve: Simplifying -1 + 2s2 + -1s4 + n4 = 0 Reorder the terms: -1 + n4 + 2s2 + -1s4 = 0 Solving -1 + n4 + 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 + n4 + 2s2 + 1 + -1s4 = 0 + 1 Reorder the terms: -1 + 1 + n4 + 2s2 + -1s4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + n4 + 2s2 + -1s4 = 0 + 1 n4 + 2s2 + -1s4 = 0 + 1 Combine like terms: 0 + 1 = 1 n4 + 2s2 + -1s4 = 1 Add '-1n4' to each side of the equation. n4 + 2s2 + -1n4 + -1s4 = 1 + -1n4 Reorder the terms: n4 + -1n4 + 2s2 + -1s4 = 1 + -1n4 Combine like terms: n4 + -1n4 = 0 0 + 2s2 + -1s4 = 1 + -1n4 2s2 + -1s4 = 1 + -1n4 Add '-2s2' to each side of the equation. 2s2 + -2s2 + -1s4 = 1 + -1n4 + -2s2 Combine like terms: 2s2 + -2s2 = 0 0 + -1s4 = 1 + -1n4 + -2s2 -1s4 = 1 + -1n4 + -2s2 Add 's4' to each side of the equation. -1s4 + s4 = 1 + -1n4 + -2s2 + s4 Combine like terms: -1s4 + s4 = 0 0 = 1 + -1n4 + -2s2 + s4 Simplifying 0 = 1 + -1n4 + -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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