we can pretty much use any of the 3 double-angle identities for cosine, so
[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{let's use this one}
\end{cases}\\\\
-------------------------------\\\\
cos(2x)+sin(x)\implies 2cos^2(x)-1+sin(x) [/tex]
