The identity is verified. $cos^4-sin^4x=cos~2x$
Work Step by Step
Use: $cos^2x+sin^2x=1$ and $cos~2x=cos^2x-sin^2x$ Start on the left side: $cos^4-sin^4x=(cos^2x)^2-(sin^2x)^2=(cos^2x+sin^2x)(cos^2x-sin^2x)=(1)~(cos~2x)=cos~2x$
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