The value of $ an \left(\frac{\pi}{8} ight)$ is

Question

The value of $	an \left(\frac{\pi}{8}ight)$ is

Aicharya · Accepted Answer

Since, $	an \frac{A}{2}=\frac{1-\cos A}{\sin A}$ Putting $\frac{\mathrm{A}}{2}=\frac{\pi}{8}$, we get $\begin{aligned} 	an \left(\frac{\pi}{8}ight) & =\frac{1-\cos \frac{\pi}{4}}{\sin \frac{\pi}{4}} \ & =\frac{1-\frac{1}{\sqrt{2}}}{\left(\frac{1}{\sqrt{2}}ight)} \ 	herefore \quad 	an \left(\frac{\pi}{8}ight) & =\sqrt{2}-1\end{aligned}$

The value of $\tan \left(\frac{\pi}{8}\right)$ is

Solution