Prove that SinA/(1+CosA)+SinA/(1-SinA)=2CosecA
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First of all taking LHS,
= sinA/1+cosA + 1+cosA/sinA
= [sin^2A + (1 + cosA)^2]/sinA(1 + cosA)
= (sin^2A + 1 + cos^2A + 2cosA)/sinA(1 + cosA)
= (1 + 1 + 2cosA) / sinA(1 + cosA) [ ∵ as sin^2A + cos^2A = 1]
= (2 + 2cosA) / sinA(1 + cosA)
= 2(1 + cosA)/sinA(1 + cosA)
= 2/sinA = 2 cosecA [since 1/sinA
= cosecA]
= R.H.S.
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