求证1/sinA+1/cosA=sinA(1+tanA)+cosA(1+1/tanA)

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求证1/sinA+1/cosA=sinA(1+tanA)+cosA(1+1/tanA)
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求证1/sinA+1/cosA=sinA(1+tanA)+cosA(1+1/tanA)
求证1/sinA+1/cosA=sinA(1+tanA)+cosA(1+1/tanA)

求证1/sinA+1/cosA=sinA(1+tanA)+cosA(1+1/tanA)
sina*(1+tana)+cosa*(1+1/tana)=1/sina+1/cosa
=sina*(1+sina/cosa)+cosa*(1+cosa/sina)
=sina+sin^2/cosa+cos^2a/sina+cosa
=sina+cosa+[(sin^3a+cos^a)/sinacosa]
=sina+cosa+[(sina+cosa)(sin^2a+cos^2a-sinacosa)/sinacosa]
=sina+cosa+[(sina+cosa)(1-sinacosa)/sinacosa]
=sina+cosa+(sina+cosa)/sinacosa-sina-cosa
=(sina+cosa)/sinacosa
=1/sina+1/cosa