Question

`sqrt((1-cos theta)/(1+cos theta)) = (cosec  theta - cot  theta)`

Answer 1

LHS = `sqrt((1-cos theta)/(1+ cos theta))`

      =`sqrt(((1-cos theta))/((1+cos theta)) xx ((1- cos theta))/((1 - cos theta))`

      =`sqrt((1-cos theta)^2 / (1-cos^2 theta))`

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

     =`(1-cos theta)/sin theta`

     =`1/sin theta - cos theta/ sin theta`

     =(𝑐𝑜𝑠𝑒𝑐 𝜃 − cot 𝜃)
      = RHS