Question

Find the value of $\cos x$ if $0<x<\frac{\pi }{2}$ and $\tan x=\frac{a}{2}$

• A. $\frac{2}{\sqrt{a^2-4}}$
• B. $\frac{a}{\sqrt{a^2-4}}$
• C. $\frac{2}{a+2}$
• D. $\frac{2}{\sqrt{a^2+4}}$
• E. $\frac{a}{\sqrt{a^2+4}}$

Answer 1

The correct option is D $\frac{2}{\sqrt{a^2+4}}$

Given, $\tan x=\frac{a}{2}$

Then perpendicular is $a$ and hypotenuse is $2$.

Then base $=$ $\sqrt{(a{)}^2+(2{)}^2}=\sqrt{a^2+4}$

Then $\cos x=\frac{hypotenuse}{base}=\frac{2}{\sqrt{a^2+4}}$