Question

$\frac{\tan \Theta }{\sec \Theta -1}+\frac{\tan \Theta }{sec\Theta +1}$ is equal to

• A. $cosec\Theta$
• B. $2cosec\Theta$
• C. $sec\Theta$
• D. $2sec\Theta$

Answer 1

The correct option is B $2cosec\Theta$

$\frac{\tan \theta }{\sec \theta -1}+\frac{\tan \theta }{\sec \theta +1}$
$=\tan \theta \left\{\frac{(\sec \theta +1)+(\sec \theta -1)}{{\sec }^2\theta -1}\right\}$
$=\frac{\tan \theta .2\sec \theta }{{\tan }^2\theta }=2.\frac{\sec \theta }{\tan \theta }=2cosec\theta$