# How do you verify Cos(180° - theta) = -cos theta?

May 23, 2016

#### Explanation:

One of the easiest ways could be to use the formula

$\cos \left(A - B\right) = \cos A \cos B + \sin A \sin B$

Hence, $\cos \left({180}^{o} - \theta\right) = \cos {180}^{o} \cos \theta + \sin {180}^{o} \sin \theta$

= $\left(- 1\right) \times \cos \theta + 0 \times \sin \theta$

= $- \cos \theta$