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$\sqrt{2+\sqrt{2+2 \cos 4 \theta}}=$
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Verified Answer
The correct answer is:
$2 \cos \theta$
$\begin{aligned}
& \sqrt{2+\sqrt{2+2 \cos 4 \theta}}=\sqrt{2+\sqrt{2.2 \cos ^2 2 \theta}} \\
& =\sqrt{2+2 \cos 2 \theta}=\sqrt{4 \cos ^2 \theta}=2 \cos \theta
\end{aligned}$
& \sqrt{2+\sqrt{2+2 \cos 4 \theta}}=\sqrt{2+\sqrt{2.2 \cos ^2 2 \theta}} \\
& =\sqrt{2+2 \cos 2 \theta}=\sqrt{4 \cos ^2 \theta}=2 \cos \theta
\end{aligned}$
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