Question

Rewrite with only sin x and cos x. cos 2x + sin x

Answer 1

we can pretty much use any of the 3 double-angle identities for cosine, so

$\bf \textit{Double Angle Identities} \\\\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ 1-2sin^2(\theta)\\ 2cos^2(\theta)-1&\leftarrow \textit{let's use this one} \end{cases}\\\\ -------------------------------\\\\ cos(2x)+sin(x)\implies 2cos^2(x)-1+sin(x)$