trigonometry - Proving $left(tan^2x +frac{1}{tan x}right) left(sin x+cos xright)=left(frac{1}{cos x}right)+left(frac{1}{sin x}right)$

$$
\left(\tan^2x +\frac{1}{\tan x}\right) \left(\sin x+\cos x\right)=\left(\frac{1}{\cos x}\right)+\left(\frac{1}{sin x}\right)
$$

Can someone show me how to solve this identity and also explain the steps?