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prove that sinA/(1+cosA) + (1+cosA)/(sinA) = 2cosecA

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(sinA/1+cosA)+(1+cosA/sinA) = 2cscA?
Work on LHS
sinA/(1+cosA)+(1+cosA)/sinA
=[sin^2A + (1 + cosA)^2]/[sinA(1 + cosA)]
=[sin^2A + 1 + 2cosA + cos^2A]/[sinA(1 + cosA)]
=[(sin^2A + cos^2A) + 1 + 2cosA]/[sinA(1 + cosA)]
=[1 + 1 + 2cosA]/[sinA(1 + cosA)]
=[2 + 2cosA]/[sinA(1 + cosA)]
=[2(1 + cosA)]/[sinA(1 + cosA)]
=2/sinA
=2(1/sinA)
=2cscA

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