Question

Find the value of
$\frac{1}{\sec \theta -\tan \theta }+\frac{1}{\sec \theta +\tan \theta }$

• A. $2\sec \theta$
• B. $2\cos \theta$
• C. $2\tan \theta$
• D. $2cosec\theta$

Answer 1

The correct option is A $2\sec \theta$

Simplifying the given expression, we get
$\frac{1}{sec\theta +tan\theta }+\frac{1}{sec\theta -tan\theta }$
$=\frac{sec\theta -tan\theta +sec\theta +tan\theta }{se{c}^2\theta -ta{n}^2\theta }$
$=\frac{2sec\theta }{1}$
$=2sec\theta$