## Precalculus (6th Edition) Blitzer

The exact value of $1-2{{\sin }^{2}}\frac{\pi }{12}$ is $\frac{\sqrt{3}}{2}$.
Recall the given expression. $\cos 2\theta =1-2{{\sin }^{2}}\theta$ Apply the given expression. \begin{align} & 1-2{{\sin }^{2}}\frac{\pi }{12}=\cos 2\left( \frac{\pi }{12} \right) \\ & =\cos \left( \frac{\pi }{6} \right) \\ & =\frac{\sqrt{3}}{2} \end{align} Therefore, the exact value of $1-2{{\sin }^{2}}\frac{\pi }{12}$ is $\frac{\sqrt{3}}{2}$.