## Precalculus (6th Edition) Blitzer

We have $\tan x+\frac{1}{\tan x}=\frac{1}{\sin x\cos x}$ By evaluating the left side, \begin{align} & \text{Left side}=\tan x+\frac{1}{\tan x} \\ & =\frac{{{\tan }^{2}}x+1}{\tan x} \\ & =\frac{{{\sec }^{2}}x}{\tan x} \\ & =\frac{{}^{1}/{}_{{{\cos }^{2}}x}}{{\sin x}/{\cos x}\;} \end{align} $=\frac{1}{\sin x\cos x}$ Thus, $\text{left side = right side}$. So, we can say that the identity is true. Hence, verified.