1 Answer

Goldsky · Answer 1 · 2023-01-16T02:25:30+0000

we have that

The double angles formula is equal to

$\cos (2\theta)=\cos ^2(\theta)-\sin ^2(\theta)$

and remember that

$\begin{gathered} \sin ^2(\theta)+\cos ^2(\theta)=1 \\ \cos ^2(\theta)=1-\sin ^2(\theta) \end{gathered}$

therefore

substitute in the original expression

$\begin{gathered} \cos (2\theta)=1-\sin ^2(\theta)-\sin ^2(\theta) \\ \cos (2\theta)=1-2\sin ^2(\theta) \end{gathered}$

therefore

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