Question

tan(pi/8)
Evaluate using half angle identities?
Show work please?

Answer 1

\[ \tan \frac{x}{2} = \frac{\sin x}{1+\cos x}\]

Let
\[x = \frac{\pi}{4} \implies \frac{x}{2} = \frac{\pi}{8} \]

and note:
\[\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}} \]