Question

Use basic identities to simplify the expression. csc(theta)*cot(theta)/sec(theta)

Answer 1

We have the expression

$\frac{\csc (\theta)\cdot\cot (\theta)}{\sec (\theta)}$

In order to simplify it, we have to look at some trigonometric identities:

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

Then, we can write:

$\frac{1}{\sin(\theta)}\cdot\frac{\cos(\theta)}{\sin(\theta)}\cdot\cos (\theta)=\frac{\cos(\theta)^2}{\sin(\theta)^2}=\cot ^2(\theta)$

The simplified expression is cot^2(theta)

$\cot ^2(\theta)$