求证sinθ(1+tanθ)+cosθ(1+1/tanθ)=1/sinθ+1/cosθ
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求证sinθ(1+tanθ)+cosθ(1+1/tanθ)=1/sinθ+1/cosθ
求证sinθ(1+tanθ)+cosθ(1+1/tanθ)=1/sinθ+1/cosθ
求证sinθ(1+tanθ)+cosθ(1+1/tanθ)=1/sinθ+1/cosθ
sinθ(1+tanθ)+cosθ(1+1/tanθ)
=sinθ+sin²θ/cosθ+cosθ+cos²θ/sinθ
=(sinθ+cos²θ/sinθ)+(cosθ+sin²θ/cosθ)
=(sin²θ+cos²θ)/sinθ+(sin²θ+cos²θ)/cosθ
=1/sinθ+1/cosθ
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