## Precalculus (6th Edition) Blitzer

${{\sin }^{2}}x+\cos 2x={{\cos }^{2}}x$ Consider the left side of the given expression and apply the double angle formula. \begin{align} & {{\sin }^{2}}x+\cos 2x={{\sin }^{2}}x+{{\cos }^{2}}x-{{\sin }^{2}}x \\ & ={{\cos }^{2}}x \end{align} Hence, it is proved that the given identity ${{\sin }^{2}}x+\cos 2x={{\cos }^{2}}x$ holds true.