Question

`sec theta (1- sin theta )( sec theta + tan theta )=1`

Answer 1

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

       =` (sec theta - sec theta sin theta) ( sec theta + tan theta)`

       =` (sec theta - 1/(cos theta) xx sin theta )(sec theta+tantheta)`

       =` (sec theta - tan theta ) ( sec theta + tan theta)`

      = `sec ^2 theta - tan ^2 theta`

     =  1

     = RHS