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

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  1. (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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