Question

`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`

Answer 1

LHS = `cos theta/((1-tan theta))-sin^2theta/((cos theta-sintheta))`

       =`cos theta/((1-sintheta/costheta)) -sin^2 theta/((cos theta-sin theta))`

     =`cos^2 theta/((cos theta-sintheta))- sin^2 theta/((cos theta-sin theta))`

     =`(cos^2 theta- sin ^2 theta)/((cos theta- sin theta))`

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

   =`(cos theta + sin theta)`

   = RHS
Hence, LHS = RHS