## Precalculus (6th Edition) Blitzer

By solving the left side of the identity, we get: $\cot x+\tan x=\left( \csc x \right)\left( \sec x \right)$: \begin{align} & \cot x+\tan x=\frac{\cos x}{\sin x}+\frac{\sin x}{\cos x} \\ & =\frac{{{\cos }^{2}}x+{{\sin }^{2}}x}{\sin x\cos x} \\ & =\frac{1}{\sin x\cos x} \\ & =\frac{1}{\sin x}\times \frac{1}{\cos x} \end{align} Therefore, $\cot x+\tan x=\left( \csc x \right)\left( \sec x \right)$ Thus, the solution is that the identity is correct.