Question

Prove that SinA/(1+CosA)+SinA/(1-SinA)=2CosecA

Answer 1

Answer:

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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Answer 2

Step-by-step explanation:

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