Question

What is the exact value of $\sec \left(\frac{\mathrm{\pi }}{4}\right)$?

Answer 1

Find the value of $\sec \left(\frac{\mathrm{\pi }}{4}\right)$:

We know that $\sec \theta =\frac{1}{\cos \theta }$.

Using the above property, we get

$\sec \left(\frac{\mathrm{\pi }}{4}\right)=\frac{1}{\cos \left({\displaystyle \frac{\mathrm{\pi }}{4}}\right)}$

$\Rightarrow$ $\sec \left(\frac{\mathrm{\pi }}{4}\right)=\frac{1}{{\displaystyle \frac{1}{\sqrt{2}}}}$ $\left[\because \cos \left(\frac{\mathrm{\pi }}{4}\right)=\frac{1}{\sqrt{2}}\right]$

$\Rightarrow$ $\sec \left(\frac{\mathrm{\pi }}{4}\right)=\sqrt{2}$

Hence, the exact value of $\sec \left(\frac{\mathrm{\pi }}{4}\right)$ is $\sqrt{2}$.