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Question
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
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Solution
`(cosecA)/(cotA+tanA)=cosA`
= LHS
= `(cosecA)/(cotA+tanA)`
= `(cosecA)/(cosA/sinA+sinA/cosA)`
=`((cosecA)/(cos^2A+sin^2A))/(sinA.cosA)`
= `(1/sinA)/(1/(sinA.cosA))`
= `(sinA.cosA)/sinA`
= cosA
= RHS
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