sums and differences of angles

**deltaxray** · February 20th 2010, 03:47 PM

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.

**icemanfan** · February 20th 2010, 03:53 PM

$C = \pi - A - B$

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

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 $\sin B$ .

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