# How do you verify costhetacos(-theta)-sinthetasin(-theta)=1?

Nov 17, 2016

see below

#### Explanation:

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

Use the odd and even property. That is, $\cos \left(- \theta\right) = \cos \theta$ and $\sin \left(- \theta\right) = - \sin \theta$

Left Hand : $= \cos \theta \cos \left(- \theta\right) - \sin \theta \sin \left(- \theta\right)$

$= \cos \theta \cos \left(\theta\right) + \sin \theta \sin \left(\theta\right)$

$= {\cos}^{2} \theta + {\sin}^{2} \theta$

$= 1$

$\therefore =$ Right Side