Use the half angle formula to find the exact value of

Question

tan 7 pie/8

Answer 1

tan(7pi/8) = tan(7pi/4/2)

hence
tan(7pi/8)=sin(7pi/4)/(1+cos(7pi/4))

sin(7pi/4)=-(root2)/2
cos(7pi/4)=(root2)/2

so
tan(7pi/8)= -(root2)/2/(1+(root2)/2)

and then tidy up.

Sorry about the expressions, not easy to do in text.

Answer 2

How do you tidy it up?