Question

`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`

Answer 1

LHS = `(tan theta)/((sec theta -1)) + (tan theta)/((sec theta +1))`

      =`tan theta {(sec^theta +1+ sec theta-1)/((sec theta -1)( sec theta +1))}`

       =` tan theta {(2 sec theta)/(sec^2 theta-1)}`

      =` tan theta xx(2 sec theta)/(tan^2 theta -1)`

      =`2 (sec^theta)/(tan^theta)`

     =`2 (1/cos theta)/(sin theta/cos theta)`

     =`2 1/sin theta`

    =`2 cosec  theta`

    = RHS
Hence, LHS = RHS