Question

\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to 

Options

• 2 tan θ

•  2 sec θ

•  2 cosec θ

•  2 tan θ sec θ

Answer 1

The given expression is  `tan θ /(secθ-1)+tan θ/(sec θ+1)`

=` (tan θ (sec θ+1)+tan θ(secθ-1))/((secθ-1)(secθ+1))`

= `(tan θ sec θ+tanθ+tan θ secθ-tan θ)/(sec^2θ-1)`

=`( 2tanθ secθ)/tan^2θ`

=`(2secθ)/tan θ` 

= `(2 1/cos θ)/(sinθ/cos θ)` 

=`2 1/ sinθ`

= `2 cosec θ`