## Precalculus (6th Edition) Blitzer

The given expression on the right side $2\sin t\cos t\sec 2t$ can be simplified by applying the double angle formula $\sin 2\theta =2\sin \theta \cos \theta$, reciprocal identity $\sec x=\frac{1}{\cos x}$, and the quotient identity $\tan x=\frac{\sin x}{\cos x}$. Therefore, the expression will be: \begin{align} & 2\sin t\cos t\sec 2t=\sin 2t.\frac{1}{\cos 2t} \\ & =\frac{\sin 2t}{\cos 2t} \\ & =\tan 2t \end{align} Hence, the expression on the left-side is equal to the expression on the right-side.