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