Question

If $\tan \theta +\sec \theta =\frac{2}{3}$ then $\sec \theta$ is

• A. $\frac{13}{2}$
• B. $\frac{1}{12}$
• C. $\frac{13}{12}$
• D. $\frac{11}{12}$

Answer 1

The correct option is C $\frac{13}{12}$

$\tan \theta +\sec \theta =\frac{2}{3}$..........(1) Given..

We know that,

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

$⟹(\sec \theta -\tan \theta )(\sec \theta +\tan \theta )=1$

$⟹(\sec \theta -\tan \theta )\left(\frac{2}{3}\right)=1$

$⟹(\sec \theta -\tan \theta )=\frac{3}{2}$

$\tan \theta +\sec \theta =\frac{2}{3}$ .......(2)

Adding (1) and (2), we get

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

$⟹\sec \theta =\frac{13}{12}$