Question

If $sec\left(\theta \right)$ is $\frac{5}{4}$ then write the value of $\cos \left(\theta \right)$?

Answer 1

Computing the required value:

Given that: $\sec \left(\theta \right)=\frac{5}{4}$

We need to find the value of $\cos \left(\theta \right)$,

According to the trigonometric reciprocal formula we know that,

$\Rightarrow \sec \left(\theta \right)=\frac{1}{\cos \left(\theta \right)}$

Substituting the given value of $\sec \left(\theta \right)$ in the above equation, we get

$$\begin{gathered} \Rightarrow sec\left(\theta \right)=\frac{1}{\cos \left(\theta \right)} \\ \Rightarrow \frac{5}{4}=\frac{1}{\cos \left(\theta \right)} \\ \Rightarrow \cos \left(\theta \right)=\frac{4}{5} \end{gathered}$$

Hence, the value of $\cos \left(\theta \right)=\frac{4}{5}$.