## Precalculus (6th Edition) Blitzer

To verify the given identity, ${{\cos }^{2}}x-{{\sin }^{2}}x=1-2{{\sin }^{2}}x$ Recall Trigonometric Identity, ${{\sin }^{2}}x+{{\cos }^{2}}x=1$ Use the above identity and solve the left side of the given expression, \begin{align} & {{\cos }^{2}}x-{{\sin }^{2}}x=\left( 1-{{\sin }^{2}}x \right)-{{\sin }^{2}}x \\ & =1-2{{\sin }^{2}}x \end{align} Hence, it is proved that the given identity holds true.