若tanα=根号下2,求值2×(sinα)^2-sinαcosα+(cosα)^2.

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若tanα=根号下2,求值2×(sinα)^2-sinαcosα+(cosα)^2.

若tanα=根号下2,求值2×(sinα)^2-sinαcosα+(cosα)^2.
若tanα=根号下2,求值2×(sinα)^2-sinαcosα+(cosα)^2.

若tanα=根号下2,求值2×(sinα)^2-sinαcosα+(cosα)^2.
2×(sinα)^2-sinαcosα+(cosα)^2=(2×(sinα)^2-sinαcosα+(cosα)^2)/((sinα)^2+(cosα)^2),
再上下同时除以(cosα)^2,可得2×(sinα)^2-sinαcosα+(cosα)^2=(2×(tanα)^2-tanα+1)/(1+(tanα)^2);带入tanα=根号下2,得
2×(sinα)^2-sinαcosα+(cosα)^2=(5-根号下2)/3

2×(sinα)^2-sinαcosα+(cosα)^2
=[2×(sinα)^2-sinαcosα+(cosα)^2]/[(sinα)^2+(cosα)^2]
=2(tana)^2-tana+1/(tanα)^2+1
=(4-√2+1)/3=(5-√2)/3