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Question
Prove that `"cosec" θ xx sqrt(1 - cos^2θ) = 1`.
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Solution
L.H.S. = `"cosec" θ xx sqrt(1 - cos^2θ)`
= `"cosec" θ xx sqrt(sin^2θ)` ...`[(∵ sin^2θ + cos^2θ = 1),(therefore 1 - cos^2θ = sin^2θ)]`
= cosec θ × sin θ
= 1 ...[∵ sin θ × cosec θ = 1]
= R.H.S.
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