Q. Find $ \cos \,(x/2), $ if $ \tan \,x=5/12,\,x $ in quadrant III
J & K CETJ & K CET 2014
Solution:
Given, $ \tan x=\frac{5}{12} $ and x is in II quadrant.
$ \therefore $ $ \sin x=\frac{-5}{13} $ and $ \cos x=\frac{-12}{13} $
Now, $ \cos x=2{{\cos }^{2}}\frac{x}{2}-1 $
$ \Rightarrow $ $ {{\cos }^{2}}\frac{x}{2}=\frac{1}{2}(\cos x+1) $
$=\frac{1}{2}\left( \frac{-12}{13}+1 \right) $
$=\frac{1}{2}\left( \frac{1}{13} \right)=\frac{1}{26}\,\,\Rightarrow \cos \frac{x}{2}=\sqrt{\frac{1}{26}} $
