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

The correct option is C $\frac{1}{\sqrt{2}+1}$

For any angle $A$,
$\tan \frac{A}{2}=\frac{\sin \frac{A}{2}}{\cos \frac{A}{2}}=\frac{2\sin \frac{A}{2}\cos \frac{A}{2}}{2{\cos }^2\frac{A}{2}}$
$=\frac{\sin A}{1+\cos A}$
$\therefore \tan \frac{\pi }{8}=\frac{\sin \frac{\pi }{4}}{1+\cos \frac{\pi }{4}}=\frac{1}{\sqrt{2}+1}$