Question

What is the exact value of $\sec \left(45°\right)$?

Answer 1

Find the exact value of $\sec \left(45°\right)$

We know that, $\mathit{s}\mathit{e}\mathit{c}\left(\theta \right)\mathbf{=}\frac{\mathbf{1}}{\mathbf{c}\mathbf{o}\mathbf{s}\left(\theta \right)}$ and $\cos \left(45°\right)=\frac{1}{\sqrt{2}}$

Use the result to calculate the exact value of $\sec \left(45°\right)$:

$\begin{array}{rcl}\sec \left(45°\right)& =& \frac{1}{\cos \left(45°\right)}\\ & \Rightarrow & \sec \left(45°\right)=\frac{1}{{\displaystyle \frac{1}{\sqrt{2}}}}\\ & \Rightarrow & \sec \left(45°\right)=\sqrt{2}\end{array}$

Hence, the required exact value is $\sec \left(45°\right)=\sqrt{2}$