Question

prove that(1-cosa)(1+sina)=sin^2a

Answer 1

We know that sin2θ+cos2θ=1

i.e. 1-cos2θ=sin2θ

∴(1-cosθ)(1+cosθ)=sinθ.sinθ

 

∴1-cosθsinθ=sinθ1+cosθ, OR    sinθ1+cosθ=1-cosθsinθ (by theorem on equal ratios)=(1-cosθ)-(sinθ)(sinθ)-(1-cosθ)∴sinθ1+cosθ=1-cosθ-sinθsinθ-1-cosθ