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 left side $\cos 4t$ can be written as $\cos 2.2t$. As per the double angle formula, $\cos 2t=1-2{{\sin }^{2}}\theta $. Therefore, using the double angle formula:
$\begin{align}
& \cos 4t=\cos 2.2t \\
& =1-2{{\sin }^{2}}2t \\
& =1-2{{\left( 2\sin t\cos t \right)}^{2}} \\
& =1-2.4{{\sin }^{2}}t{{\cos }^{2}}t
\end{align}$
Now, the expression can be further classified as:
$1-2.4{{\sin }^{2}}t{{\cos }^{2}}t=1-8{{\sin }^{2}}t{{\cos }^{2}}t$
Hence, the expression on the left-side is equal to the expression on the right-side.
