How do you prove $(cos2A)/sinA + (sin2A)/cosA = csc A$ ?

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Answer 1 · 2018-07-12T13:27:44

Please refer to a Proof in the Explanation.

$(cos2A)/sinA+(sin2A)/cosA$ ,

$=(cos2AcosA+sin2AsinA)/(sinAcosA)$ ,

$=(cos(2A-A))/(sinAcosA)$ ,

$=cosA/(sinAcosA)$ ,

$=1/sinA$ ,

$=cscA$ , as desired!

Answer 2 · 2018-07-12T18:32:22

Please refer to a Second Proof in Explanation.

$"Using "cos2A=1-2sin^2A, and, sin2A=2sinAcosA$ ,

$"The L.H.S."=(1-2sin^2A)/sinA+(2sinAcosA)/cosA$ ,

$=1/sinA-(2sin^2A)/sinA+2sinA$ ,

$=cscA-2sinA+2sinA$ ,

$=cscA$ ,

$="The R.H.S."$

How do you prove (cos2A)/sinA + (sin2A)/cosA = csc A(cos2A)/sinA + (sin2A)/cosA = csc A?