Answer
The expression on the left-side is equal to the expression on the right-side.
Work Step by Step
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.
