Question

If $\sec \Theta -\tan \Theta =k,$ then the value of $\sec \Theta +\tan \Theta$ is

• A. (1-k)
• B. (1+k)
• C. $\frac{1}{k}$
• D. $1-\frac{1}{k}$

Answer 1

Answer: (C)

$\frac{1}{k}$

given , $\sec \theta -\tan \theta =k$ .....(i)
Also , ${\sec }^2\theta -{\tan }^2\theta =1$ .....(ii)
Dividing equation (ii) by (i) , we get
$\frac{{\sec }^2\theta -{\tan }^2\theta }{\sec \theta -\tan \theta }=\frac{1}{k}$
or $\sec \theta +\tan \theta =\frac{1}{k}$