# Question #a0e09

Oct 10, 2016

Use that sine is an odd function, cosine is an even function, and the identity ${\cos}^{2} \left(\theta\right) + {\sin}^{2} \left(\theta\right) = 1$

#### Explanation:

We will use the following:

• ${\cos}^{2} \left(\theta\right) + {\sin}^{2} \left(\theta\right) = 1$
• $\cos \left(- \theta\right) = \cos \left(\theta\right)$
• $\sin \left(- \theta\right) = - \sin \left(\theta\right)$

With those,

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

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

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

$= {\cos}^{2} \left(\theta\right) + {\sin}^{2} \left(\theta\right)$

$= 1$