Chapter 7 - Section 7.1 - Trigonometric Identities - 7.1 Exercises - Page 543: 33

$\dfrac{\cos u\sec u}{\tan u}=\cot u$

$\dfrac{\cos u\sec u}{\tan u}=\cot u$ Substitute $\sec u$ with $\dfrac{1}{\cos u}$ and $\tan u$ with $\dfrac{\sin u}{\cos u}$. Then simplify: $\dfrac{\cos u\Big(\dfrac{1}{\cos u}\Big)}{\Big(\dfrac{\sin u}{\cos u}\Big)}=\cot u$ $\dfrac{1}{\Big(\dfrac{\sin u}{\cos u}\Big)}=\cot u$ $\dfrac{\cos u}{\sin u}=\cot u$ $\cot u=\cot u$