Prove that cosecθ √1 − cos2 θ =1.

1.	Prove that cosecθ √1 − cos2 θ =1.
Answer» Identity : sin²θ+cos²θ = 1 LHS = cosec θ \(\sqrt{(1-cos^2\theta)}\) = cosec θ\(\sqrt{sin^2\theta}\) = cosec θ sin θ = \(\frac1{sin\theta}\times sin\theta\) = 1 = RHS

Answer»

Identity : sin²θ+cos²θ = 1

LHS = cosec θ \(\sqrt{(1-cos^2\theta)}\)

= cosec θ\(\sqrt{sin^2\theta}\)

= cosec θ sin θ

= \(\frac1{sin\theta}\times sin\theta\)

= 1

= RHS

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Prove that cosecθ √1 − cos2 θ ​ =1.

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Prove that cosecθ √1 − cos2 θ =1.