Question

Find $\cos (x/2),$ if $\tan x=5/12,x$ in quadrant III

• A. $5/\sqrt{13}$
• B. $5/\sqrt{26}$
• C. $5/13$
• D. $5/26$

Answer 1

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, $\cos x=2{\cos }^2\frac{x}{2}-1$
$\Rightarrow$ ${\cos }^2\frac{x}{2}=\frac{1}{2}(\cos x+1)$
$=\frac{1}{2}\left(\frac{-12}{13}+1\right)$
$=\frac{1}{2}\left(\frac{1}{13}\right)=\frac{1}{26}\Rightarrow \cos \frac{x}{2}=\sqrt{\frac{1}{26}}$