# How do you evaluate cos((3pi)/5)cos((4pi)/15)+sin((3pi)/5)sin((4pi)/15)?

Feb 13, 2015

Use the standard trig. formula:
$\cos \left(a - b\right) = \cos \left(a\right) \cdot \cos \left(b\right) + \sin \left(a\right) \cdot \sin \left(b\right)$

$\cos \left(\frac{3 \Pi}{5}\right) \cos \left(\frac{4 \Pi}{15}\right) + \sin \left(\frac{3 \Pi}{5}\right) \sin \left(\frac{4 \Pi}{15}\right)$ becomes

$\cos \left(\frac{3 \Pi}{5} - \frac{4 \Pi}{15}\right)$

$= \cos \left(\frac{5 \Pi}{15}\right) = \cos \left(\frac{\Pi}{3}\right)$

$\frac{\Pi}{3}$ (${60}^{o}$) is one of the standard triangles

#cos(Pi/3) = 1/2