Question

Find the exact value by using a half-angle identity.

tangent of seven pi divided by eight.

Answer 1

\(\large \tan \dfrac{7 \pi}{8} = \tan \dfrac{\frac{7 \pi}{4}}{2}\)

Answer 2

\(\tan \dfrac{\theta}{2} = \dfrac{1 - \cos \theta}{\sin \theta} \)

\(\cos \dfrac{7\pi}{4} \) and \(\sin \dfrac{7\pi}{4} \) are well known.

Answer 3

1-sqrt2