## anonymous 5 years ago tan(pi/8) Evaluate using half angle identities? Show work please?

$\tan \frac{x}{2} = \frac{\sin x}{1+\cos x}$ Let $x = \frac{\pi}{4} \implies \frac{x}{2} = \frac{\pi}{8}$ and note: $\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}$