已知tanα=-1/2,则(1+2sinαcosα)/(sin^2-cos^2)的值为_________.

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已知tanα=-1/2,则(1+2sinαcosα)/(sin^2-cos^2)的值为_________.
已知tanα=-1/2,则(1+2sinαcosα)/(sin^2-cos^2)的值为_________.

已知tanα=-1/2,则(1+2sinαcosα)/(sin^2-cos^2)的值为_________.
(1+2sinαcosα)/(sin^2-cos^2)
=(sin²a+cos²a+2sinacosa)/(sina-c0sa)(sina+cosa)
=(sina+cosa)²/(sina-cosa)(sina+cosa)
=(sina+cosa)/(sina-cosa)
tana=-1/2
分子分母同时除以cosa得
=(tana+1)/(tana-1)
=(1/2)/(-3/2)
=-1/3

(1+2sinαcosα)/(sin^2-cos^2)
=﹙sin²a+2sinαcosα+cos²a﹚/(sin²a-cos²a)
=﹙sina+cosa﹚²/(sin²a-cos²a)
=﹙sina+cosa﹚/(sina-cosa)
=﹙tana+1﹚/﹙tana-1﹚
=后面你带入算就可以了

tanα = sinα/cosα =-1/2 所以 cosα=-2sinα
(1+2sinαcosα)/(sin^2-cos^2)=(sin^2+cos^2+2sinαcosα)/(sinα+cosα)(sinα-cosα)
=(sinα+cosα)(sinα+cosα)/(sinα+cosα)(sinα-cosα)
=(sinα+cosα)/(sinα-cosα)
=-sinα/3sinα
=—1/3