Question

Perform the indicated operations and simplify the result so there are no quotients.

Answer 1

Given an expression:

$\csc \theta(\sin \theta+\cos \theta)$

We have to simplify the given expression.

$\begin{gathered} \csc \theta(\sin \theta+\cos \theta)=\csc \theta\sin \theta+\csc \theta\cos \theta \\ =\frac{1}{\sin\theta}\cdot\sin \theta+\frac{1}{\sin\theta}\cdot\cos \theta \\ =1+\frac{\cos \theta}{\sin \theta} \\ =1+\cot \theta \end{gathered}$

Thus, the answer is 1 + cot theta.