Prove that : 1 - (Cos^2 θ)/(1 + Sin θ) = Sin θ - Mathematics

Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.

Sum

LHS = `1 - (cos^2 θ)/(1 + sin θ)`

= `1 - (1 - sin^2 θ)/(1 + sin θ)`

= `1 - ((1 - sin θ)(1 + sin θ))/(1 + sin θ)`

= 1 - ( 1 - sin θ )
= 1 - 1 + sin θ
= sin θ
= RHS
Hence proved.

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