Prove the following identities: `(cos e ctheta-cottheta)^2=(1-costheta)/(1+costheta)`

Explanation

LHS `= ({cosec} theta-cot theta)^2`


`=(frac{1}{sin theta}-frac{cos theta}{sin theta})^2`


`=(frac{1-cos theta}{sin theta})^2`


`= frac{(1-cos theta)^{2}}{sin ^{2} theta}=frac{(1-cos theta)^{2}}{1-cos theta} quad[sin ^{2} theta=1-cos ^{2} theta] `


`= frac{(1-cos theta)^{2}}{(1-cos theta)(1+cos theta)}`


`=frac{1-cos theta}{1+cos theta} `


=RHS