Question

If $\sec \left(\theta \right)=4$, how do you use the reciprocal identity to find $\cos \left(\theta \right)$?

Answer 1

Computing the required value:

Given: $sec\theta =4$

By reciprocal identity, we know that,

$$\begin{gathered} \Rightarrow sec\left(\theta \right)=\frac{1}{\cos \left(\theta \right)} \\ \Rightarrow 4=\frac{1}{\cos \left(\theta \right)} \\ \Rightarrow \cos \left(\theta \right)=\frac{1}{4} \end{gathered}$$

Hence, the value of $\cos \left(\theta \right)$ is $\frac{1}{4}$.