Question

Simplify the trig expression csc θ cot θ——————sec θ

Answer 1

To simplify:

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

We know that,

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

Using this we get,

`\begin{gathered} (\csc\theta\cot\theta)/(\sec\theta)=((1)/(\sin\theta)\cdot(\cos\theta)/(\sin\theta))/((1)/(\cos\theta)) \\ =(1)/(\sin\theta)\cdot(\cos\theta)/(\sin\theta)*(\cos\theta)/(1) \\ =(\cos^2\theta)/(\sin^2\theta) \\ =((\cos \theta)/(\sin \theta))^2 \\ =\cot ^2\theta \end{gathered}`

Hence, the answer is,

`\cot ^2\theta`