SOLUTION: Verify the identity: {{{Sin(x)(1-2*Cos^2x+ Cos^4x) = Sin^5x}}}

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Question 172634: Verify the identity:
Sin%28x%29%281-2%2ACos%5E2x%2B+Cos%5E4x%29+=+Sin%5E5x
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Prove the identity:

Sin%28x%29%281-2%2ACos%5E2x%2B+Cos%5E4x%29+=+Sin%5E5x

Factor the expression in the parentheses:

Sin%28x%29%28%281-Cos%5E2x%29%281-Cos%5E2x%29%29+=+Sin%5E5x

Write %281-Cos%5E2x%29%281-Cos%5E2x%29 as %281-Cos%5E2x%29%5E2

Sin%28x%29%281-Cos%5E2x%29%5E2+=+Sin%5E5x

Use the identity Sin%5E2alpha%2BCos%5E2alpha=1 as 1-Cos%5E2alpha=Sin%5E2alpha

Sin%28x%29%28Sin%5E2x%29%5E2+=+Sin%5E5x

Sin%28x%29Sin%5E4x+=+Sin%5E5x

Sin%5E5x+=+Sin%5E5x

Edwin