Question

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

Answer 1

We have the expression

`(\csc (\theta)\cdot\cot (\theta))/(\sec (\theta))`

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

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

Then, we can write:

`(1)/(\sin(\theta))\cdot(\cos(\theta))/(\sin(\theta))\cdot\cos (\theta)=(\cos(\theta)^2)/(\sin(\theta)^2)=\cot ^2(\theta)`

The simplified expression is cot^2(theta)

`\cot ^2(\theta)`