`sin^2(alpha) - sin^4(alpha) = cos^2(alpha) - cos^4(alpha)` Verfiy the identity.

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Chapter 5, 5.2 - Problem 16 - Precalculus (3rd Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Verify: `sin^2(alpha)-sin^4(alpha)=cos^2(alpha)-cos^4(alpha)`

Use the pythagorean identity `sin^2(alpha)+cos^2(alpha)=1`

if `sin^2(alpha)`   is isolated the pythagorean identity is

`sin^2(alpha)=1-cos^2(alpha)`

If `cos^2(alpha)`   is isolated the pythagorean identity is 

`cos^2(alpha)=1-sin^2(alpha)`

`sin^2(alpha)-sin^4(alpha)=cos^2(alpha)-cos^4(alpha)`

`sin^2(alpha)(1-sin^2(alpha))=cos^2(alpha)-cos^4(alpha)`

`(1-cos^2(alpha))cos^2(alpha)=cos^2(alpha)-cos^4(alpha)`

`cos^2(alpha)-cos^4(alpha)=cos^2(alpha)-cos^4(alpha)`

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