已知tanθ=1/2,求2sin^2θ+3sinθcosθ﹣cos^2θ的值

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已知tanθ=1/2,求2sin^2θ+3sinθcosθ﹣cos^2θ的值

已知tanθ=1/2,求2sin^2θ+3sinθcosθ﹣cos^2θ的值
已知tanθ=1/2,求2sin^2θ+3sinθcosθ﹣cos^2θ的值

已知tanθ=1/2,求2sin^2θ+3sinθcosθ﹣cos^2θ的值
2sin^2θ+3sinθcosθ﹣cos^2θ
=(2sin^2θ+3sinθcosθ﹣cos^2θ)/(sin^2θ+cos^2θ) 分子分母同时除以cos^2θ
=(2tan^2θ+3tanθ﹣1)/(tan^2θ+1) 代入tanθ=1/2
=(1/2+3/2-1)/(1/4+1)
=4/5