## Precalculus (6th Edition) Blitzer

The required value is $\frac{1}{2}$
We have the difference formula, $\cos \alpha \cos \beta +\sin \alpha \sin \beta =\cos \left( \alpha -\beta \right)$. Now, applying the difference formula where $\alpha$ is $\frac{5\pi }{12}$ and $\beta$ is $\frac{\pi }{12}$, we get: \begin{align} & \cos \frac{5\pi }{12}\cos \frac{\pi }{12}+\sin \frac{5\pi }{12}\sin \frac{\pi }{12}=\cos \left( \frac{5\pi }{12}-\frac{\pi }{12} \right) \\ & =\cos \frac{4\pi }{12} \\ & =\cos \frac{\pi }{3} \\ & =\frac{1}{2} \end{align} Hence, the required value is $\frac{1}{2}$