Answer
$\sqrt 2+1$
Work Step by Step
Double -angle Theorem can be defined as: $\tan \dfrac{\theta}{2}=\pm \sqrt {\dfrac{1- \cos \theta}{1+ \cos \theta}}$
$\tan (-5 \pi/8)=\tan \dfrac{(-5 \pi/4)}{2}$
or, $=\sqrt {\dfrac{1- \cos (-5 \pi/4)}{1+ \cos (-5 \pi/4)}}$
or, $=\sqrt {\dfrac{1- \cos (2 \pi -5 \pi/4)}{1+ \cos (2 \pi-5 \pi/4)}}$
or, $=\sqrt {\dfrac{1- \cos (3 \pi/4)}{1+ \cos (3 \pi/4)}}$
or, $=\sqrt{\dfrac{2+\sqrt 2}{2-\sqrt 2}}$
or, $=\sqrt 2+1$
