Prove that:
\[
\begin{aligned}
\cos ^{4} \theta-\sin ^{4} \theta & ...
Prove that:
\[
\begin{aligned}
\cos ^{4} \theta-\sin ^{4} \theta & =\cos ^{2} \theta-\sin ^{2} \theta \\
& =2 \cos ^{2} \theta-1=1-2 \sin ^{2} \theta
\end{aligned}
\]
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