Question

If $\sec \theta -\tan \theta =\frac{1}{3}$, the value of $\sec \theta +\tan \theta$ is:

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C

3

We know that, ${\sec }^2\theta -{\tan }^2\theta =1$

Therefore, ($\sec \theta +\tan \theta \left)\right(\sec \theta -\tan \theta )=1$

Since, $\sec \theta -\tan \theta =\frac{1}{3}$ [Given]

$\Rightarrow (\sec \theta +\tan \theta )\times \frac{1}{3}=1$

Thus, $\sec \theta +\tan \theta =3$