## Precalculus (6th Edition) Blitzer

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.