Question

if cos theta =2/3 ,then the value of 2sec^2theta +2tan^2 theta -9 is
(a)2
(b)-2
(c)1
(d)3​

Answer 1

Answer:

The correct answer is option (b) .

Step-by-step explanation:

Given

 $\cos\theta=\dfrac{2}{3}\Rightarrow \sec\theta=\dfrac{1}{\cos\theta}=\dfrac{3}{2}$

Also using the identity $\sec^2\theta-\tan^2\theta=1$

                       $\Rightarrow \tan^2\theta=\sec^2\theta-1=\dfrac{9}{4}-1=\dfrac{5}{4}$

Therefore required answer is

                     $=2\sec^2\theta+2\tan^2\theta-9\\\\=2(\dfrac{9}{4})+2(\dfrac{5}{4})-9\\\\=7-9=-2$