Prove that cosA/1+sinA=secA-tanA

LHS = cosA/(1+sinA)

Multiplying and dividing by (1-sinA), we get, =cosA/(1+sinA) x (1-sinA)/(1-sinA) =cosA(1-sinA)/(1-sin^2 A) =cosA(1-sinA)/(cos^2 A) =(1-sinA)/(cosA) =1/cosA – sinA/cosA =secA – tanA =RHS

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