# How do you prove (sin x+ 1) / (cos x + cot x) = tan x?

Jun 23, 2018

Below

#### Explanation:

$\frac{\sin x + 1}{\cos x + \cot x} = \tan x$

LHS
$\frac{\sin x + 1}{\cos x + \cot x}$

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

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

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

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

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

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

=$\tan x$

=RHS

Therefore, $\frac{\sin x + 1}{\cos x + \cot x} = \tan x$