Question

Find the exact value by using a half-angle identity.. tan 7pi/8

Answer 1

\[
\tan \left(\frac{7 \pi }{8}\right)=\tan \left(\pi -\frac{\pi
}{8}\right)=-\tan \left(\frac{\pi }{8}\right)=\\-\frac{\sin
\left(\frac{\pi }{4}\right)}{1+\cos \left(\frac{\pi
}{4}\right)}=-\frac{1}{\sqrt{2}
\left(1+\frac{1}{\sqrt{2}}\right)}=1-\sqrt{2}
\]

Answer 2

We used the fact that
\[
\tan\left( \frac u 2 \right)=\frac{\sin(u)}{1+\cos(u)}
\]

Answer 3

Thank you! I know what formula to use I just get stuck in the solving process once i substitute everything in...

Answer 4

YW