# sums and differences of angles

• February 20th 2010, 03:47 PM
deltaxray
sums and differences of angles
If the angles A, B of triangle ABC are such that $cos A = {-4/5}$ and $cos B = {12/13}$, find without using tables the value of Cos C'

Thanks.
• February 20th 2010, 03:53 PM
icemanfan
$C = \pi - A - B$

$\cos C = \cos(\pi - A - B)$

Using identities:

$\cos C = \cos(\pi - A)\cos B + \sin(\pi - A)\sin B$

$\cos C = -\cos A \cos B + \sin A \sin B$

You should be able to calculate $\sin A$ and $\sin B$.