Question

Rewrite in terms of sine and cosine functions:$\tan \left(\theta \right)csc\left(\theta \right)$

Short answer

In terms of sine and cosine function we get,

$\frac{1}{\cos \theta }$

Step-by-step solution

Given information

We are given an trigonometric function as$\tan \left(\theta \right)c\mathrm{sc}\left(\theta \right)$

We use trigonometric formulastan(θ)=sinθcosθcscθ=1sinθ

We get,

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

Conclusion

The function in terms of sine and cosine can be given as$\frac{1}{\cos \theta }$