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Question
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
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Solution
LHS = cosecA + cotA
= `(cosecA + cotA)/1 . (cosecA - cotA)/(cosecA - cotA)`
= `(cosec^2A - cot^2A)/(cosecA - cotA) = (1 + cot^2A - cot^2A)/(cosecA - cotA)`
= `1/(cosecA - cotA)`
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Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
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= `1/(sinθ xx cosθ)` ....... ∵ `square`
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∴ L.H.S. = R.H.S.
