Question

if tan theta =root5/2 then the value of cos theta is​

Answer 1

Answer:2/3

Explanation: Refer the picture below.

Answer 2

Given:

$\tan \theta =\frac{\sqrt{5} }{2}$

We know that

$\sec^{2}\theta -\tan^{2}\theta=1$

so we have

$\sec^{2}\theta =1+\tan^{2}\theta$

$\sec^{2}\theta =1+(\frac{\sqrt{5} }{2} )^{2}$

$\sec^{2}\theta =1+\frac{5}{4}$

$\sec^{2}\theta=\frac{4+5}{4}$

$\sec^{2}\theta =\frac{9}{4}$

$\sec\theta =\sqrt{\frac{9}{4} }$

$\sec\theta=\frac{3}{2}$

So $\cos\theta=\frac{2}{3}$

Hence the value of $\cos\theta=\frac{2}{3}$