Question

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

Answer 1

𝐿𝐻𝑆 = `(tan theta)/(1+tan^2 theta )^2 +( cot theta )/(1+cot^2 theta)^2`

        =`tan theta/ ((sec^2  theta)^2) + cot theta/((cosec^2  theta) ^2)`

        =`tan theta / sec^4 theta + cottheta/(cosec^4  theta)`

        =`sin theta/cos theta xx cos^4 theta + cos theta/sin theta xx sin ^4 theta`

      =` sin  theta  cos  ^3 theta + cos theta sin  ^3 theta`

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

    =`sin theta cos theta`

    = RHS