Question

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

Answer 1

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

       =`tan^2 theta/sec^2 theta + cot^2 theta/ cosec ^2 theta    (∵ sec^2 theta - tan^2 theta = 1 and  cosec^2 theta - cot^2 theta=1)`

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

      =` sin^2 theta + cos^2 theta`

      =1 

      = RHS

Hence, LHS = RHS