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: (B)

$\sqrt{2}-1$

$\begin{array}{c}\tan \left(\frac{\pi }{8}\right)=\tan \left(\frac{180}{8}\right)\\ \tan \left(\frac{45}{2}\right)\\ \tan \frac{A}{2}=\frac{1-\cos A}{\sin A}\\ So,Now\\ \tan \frac{45}{2}=\frac{1-\cos 45}{\sin 45}\\ =\frac{1-\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}\\ =\frac{\frac{\left(\sqrt{2}-1\right)}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}\\ \tan \left(\frac{\pi }{8}\right)=\sqrt{2}-1\end{array}$