# How do you express sin(pi/12) * cos((3pi)/8 )  without products of trigonometric functions?

Mar 24, 2016

$\setminus \sin \left(\setminus \frac{\pi}{12}\right) \setminus \cos \left(3 \setminus \frac{\pi}{8}\right)$

$= \left(\frac{1}{2}\right) \left(\setminus \sin \left(11 \setminus \frac{\pi}{24}\right) - \setminus \sin \left(7 \setminus \frac{\pi}{24}\right)\right)$

#### Explanation:

Use these identities to simplify this kind of product:

$\setminus \sin \left(a\right) \setminus \sin \left(b\right)$

$= \left(\frac{1}{2}\right) \left(\setminus \cos \left(a - b\right) \setminus \cos \left(a + b\right)\right)$

$\setminus \sin \left(a\right) \setminus \cos \left(b\right)$

$= \left(\frac{1}{2}\right) \left(\setminus \sin \left(a + b\right) + \setminus \sin \left(a - b\right)\right)$

$= \left(\frac{1}{2}\right) \left(\setminus \sin \left(a + b\right) - \setminus \sin \left(b - a\right)\right)$

$\setminus \cos \left(a\right) \setminus \cos \left(b\right)$

=(1/2)(\cos(a+b)+\cos(a-b)