sin^4A-cos^4A=1-2cos^2A

$$$$\sin^4{A}-\cos^4{A}=(\sin^2{A}-\cos^2{A})(\sin^2{A}+\cos^2{A})$$\\
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$$\sin^2{A}+\cos^2{A}=1$$\\
$$\sin^2{A}-\cos^2{A}=1-\cos^2{A}-\cos^2{A}=1-2\cos^2{A}$$\\
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So, using the last two lines in the first line we have:\\
$$\sin^4{A}-\cos^4{A}=1-2\cos^2{A}$$

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