Question #23e9c

Jan 27, 2018

$\frac{\sqrt{3}}{2}$

Explanation:

The sum formula for sine says:

$\sin \left(x + y\right) = \sin \left(x\right) \cos \left(y\right) + \cos \left(x\right) \sin \left(y\right)$

For the given expression we have $x = \frac{\pi}{12}$ and $y = \frac{\pi}{4}$, so

$\sin \left(\frac{\pi}{12}\right) \cos \left(\frac{\pi}{4}\right) + \cos \left(\frac{\pi}{12}\right) \sin \left(\frac{\pi}{4}\right) = \sin \left(\frac{\pi}{12} + \frac{\pi}{4}\right)$

$\sin \left(\frac{\pi}{12} + \frac{\pi}{4}\right) = \sin \left(\frac{\pi}{12} + \frac{3 \pi}{12}\right) = \sin \left(\frac{4 \pi}{12}\right)$

$= \sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$