求证:sin^2A+cos^2A+sinAcosA/sin^2A+cos^2A=tan^2A+1+tanA/tan^2A+1

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求证:sin^2A+cos^2A+sinAcosA/sin^2A+cos^2A=tan^2A+1+tanA/tan^2A+1

求证:sin^2A+cos^2A+sinAcosA/sin^2A+cos^2A=tan^2A+1+tanA/tan^2A+1
求证:sin^2A+cos^2A+sinAcosA/sin^2A+cos^2A=tan^2A+1+tanA/tan^2A+1

求证:sin^2A+cos^2A+sinAcosA/sin^2A+cos^2A=tan^2A+1+tanA/tan^2A+1
(sin^2A+cos^2A+sinAcosA)/(sin^2A+cos^2A)(分子分母同时除以cos^2A)
=(sin^2A/cos^2A+cos^2A/cos^2A+sinAcosA/cos^2A)/(sin^2A/cos^2A+cos^2A/cos^2A)
=(sin^2A/cos^2A+1+sinA/cosA)/(sin^2A/cos^2A+1)
=(tan^2A+1+tanA)/(tan^2A+1)