Question

The value of $\tan \frac{\pi }{8}$ is equal to

• A. $\frac{1}{2}$
• B. $\sqrt{2}+1$
• C. $\frac{1}{\sqrt{2}+1}$
• D. $1-\sqrt{2}$

Answer 1

Answer: (C)

We know that, $\tan \theta =\frac{\sin 2\theta }{1+\cos 2\theta }$
$\Rightarrow \tan \frac{\pi }{8}=\frac{\sin 2(\pi /8)}{1+\cos 2(\pi /8)}$
$\Rightarrow \tan \frac{\pi }{8}=\frac{\sin (\pi /4)}{1+\cos (\pi /4)}$
$\therefore \tan \frac{\pi }{8}=\frac{\frac{1}{\sqrt{2}}}{1+\frac{1}{\sqrt{2}}}$
$=\frac{1}{\sqrt{2}+1}$