Question

establish each identity:$csc\left(\theta \right)\cos \left(\theta \right)$

Short answer

The identity can be given as$cot\left(\theta \right)$

Step-by-step solution

Given information

We are given an expression$csc\left(\theta \right)\cos \left(\theta \right)$

We use trigonometric expression csc(θ)=1sin(θ)

We get,

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

Conclusion

On establishing the identity we get,$csc\left(\theta \right)\cos \left(\theta \right)=cot\left(\theta \right)$