[tex] \bf \textit{Double Angle Identities}
\\\\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
1-2sin^2(\theta)\\
2cos^2(\theta)-1&\leftarrow \textit{we'll use this one}
\end{cases}\\\\[-0.35em]
\rule{31em}{0.25pt}\\\\
\cfrac{1+cos(2\theta )}{cos(\theta )}=2cos(\theta )\\\\[-0.35em]
~\dotfill\\\\
\cfrac{1+[2cos^2(\theta )-1]}{cos(\theta )}\implies \cfrac{2cos^2(\theta )}{cos(\theta )}\implies \cfrac{2\underline{cos(\theta )} cos(\theta )}{\underline{cos(\theta )}}\implies 2cos(\theta ) [/tex]
