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Prove each of the following identities :...

Prove each of the following identities :
` (sin theta)/((1+ cos theta)) + ((1+ cos theta))/(sin theta) = 2 "cosec" theta `

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Prove each of the following identities : (i) (1+ cos theta)(1- cos theta)(1+ cot^(2) theta)=1 (ii) "cosec" theta (1+ cos theta)("cosec" theta - cot theta)=1