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 \\ =(1)/(\sin\theta)\cdot\sin \theta+(1)/(\sin\theta)\cdot\cos \theta \\ =1+(\cos \theta)/(\sin \theta) \\ =1+\cot \theta \end{gathered}`

Thus, the answer is 1 + cot theta.