# Question #e7c45

##### 1 Answer
Jan 3, 2017

Please see explanation below.

#### Explanation:

Rewrite everything in terms of $\sin \left(x\right)$ and $\cos \left(x\right)$

$\frac{\frac{1}{\cos} x}{\left(\sin \frac{x}{\cos} x\right) + \left(\cos \frac{x}{\sin} x\right)} = \sin x$

rewrite denominator

$\frac{\frac{1}{\cos} x}{\frac{{\sin}^{2} x + {\cos}^{2} x}{\cos x \sin x}} = \sin x$

Note that ${\sin}^{2} x + {\cos}^{2} x = 1$

$\frac{\frac{1}{\cos} x}{\frac{1}{\cos x \sin x}} = \sin x$

We rewrite the fraction as follows

$\left(\frac{1}{\cos} x\right) \frac{\cos x \sin x}{1}$

The $\cos x$ cancels and we are left with

$\sin x = \sin x$