Question

`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`

Answer 1

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

          = `(1/cos theta-sin theta/cos theta)/(1/cos theta+ sin theta/cos theta)`

         =`((1-sin theta)/cos theta)/((1+ sin theta)/cos theta)`

         =`(1-sin theta)/(1+ sin theta)`

        =`((1-sin theta) (1+ sin theta))/( (1+ sin theta )(1+ sin theta))     {"Dividing the numerator and
denominator by"(1 + cos theta)}`

        =`((1-sin^2 theta))/((1+ sin theta)^2)`

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

        = RHS