Question

Establish the identity:$sec\left(\theta \right)\sin \left(\theta \right)=\tan \left(\theta \right)$

Short answer

We establish the identity$sec\left(\theta \right)\sin \left(\theta \right)=\tan \left(\theta \right)$

Step-by-step solution

Given information

We are given$sec\left(\theta \right)\sin \left(\theta \right)$

Use trigonometric formulassec(θ)=1cos(θ)

We get,

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

Conclusion

We establish the identity$sec\left(\theta \right)\sin \left(\theta \right)=\tan \left(\theta \right)$