Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 239: 56

$\tan \theta +C$

Integrate. $\int \dfrac{\csc \theta}{(\cos \theta \cot \theta)}$ Thus, we have $\int \dfrac{\csc \theta}{(\cos \theta \cot \theta)}=\int \dfrac{1/\sin \theta}{\cos \theta (\dfrac{\cos \theta}{\sin \theta})}$ or, $ =\int sec^2 \theta$ or, $=\tan \theta +C$