Question

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

Short answer

The simplified expression can be given as$\frac{1}{\sin \theta }$

Step-by-step solution

Given information

We are given a expression$cot\left(\theta \right)sec\left(\theta \right)$

We use trigonometric formulascot(θ)=cos(θ)sin(θ)sec(θ)=1cos(θ)

We get,

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

Conclusion

The simplified expression is$\frac{1}{\sin \left(\theta \right)}$.