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

Question

Prove that : $1 - \frac{\cos^{2} θ}{1 + \sin θ} = \sin θ$ .

Sum

Solution

LHS = $1 - \frac{\cos^{2} θ}{1 + \sin θ}$

= $1 - \frac{1 - \sin^{2} θ}{1 + \sin θ}$

= $1 - \frac{(1 - \sin θ) (1 + \sin θ)}{1 + \sin θ}$

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

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

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