# Can anyone help prove this trigonometric identity?

Mar 14, 2017

#### Explanation:

$\frac{{\cos}^{2} \theta - {\sin}^{2} \theta}{{\cos}^{2} \theta + \sin \theta \cos \theta}$

= $\frac{\left(\cos \theta + \sin \theta\right) \left(\cos \theta - \sin \theta\right)}{\cos \theta \left(\cos \theta + \sin \theta\right)}$

= $\frac{\cancel{\left(\cos \theta + \sin \theta\right)} \left(\cos \theta - \sin \theta\right)}{\cos \theta \cancel{\left(\cos \theta + \sin \theta\right)}}$

= $\frac{\cos \theta - \sin \theta}{\cos} \theta$

= $\cos \frac{\theta}{\cos} \theta - \sin \frac{\theta}{\cos} \theta$

= $1 - \tan \theta$