Chapter 5 - Section 5.1 - Verifying Trigonometric Identities - Exercise Set - Page 658: 5

$\tan x \csc x \cos x=1$

We need to prove the identity $\tan x \csc x \cos x=1$ Since, $\tan x=\dfrac{\sin x}{\cos x}$ Then, we have $\tan x \csc x \cos x=\dfrac{\sin x}{\cos x} \times \dfrac{1}{\sin x} \times \cos x$ $= 1$ which is the left hand side. Thus, the identity has been proved.