Answer
The expression on the left-side is equal to the expression on the right-side.
Work Step by Step
Let us consider the given expression on the left side $\sin t-\cos 2t$, which can be simplified by using the double angle formula $\cos 2t=1-2{{\sin }^{2}}t$.
$\begin{align}
& \sin t-\cos 2t=\sin t-\left( 1-2{{\sin }^{2}}t \right) \\
& =\sin t-1+2{{\sin }^{2}}t \\
& =2{{\sin }^{2}}t+\sin t-1 \\
& =\left( 2\sin t-1 \right)\left( \sin t+1 \right)
\end{align}$
Hence, the expression on the left-side is equal to the expression on the right-side.
