已知tanα=-4/3 ,求2sin^2α+sinαcosα-3cos^2α
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已知tanα=-4/3 ,求2sin^2α+sinαcosα-3cos^2α
已知tanα=-4/3 ,求2sin^2α+sinαcosα-3cos^2α
已知tanα=-4/3 ,求2sin^2α+sinαcosα-3cos^2α
2sin^2α+sinαcosα-3cos^2α
=(2sin^2α+sinαcosα-3cos^2α)/(sin^2α+cos^2α)
=(2tan^2α+tanα-3)/(tan^2α+1)
=-7/25
tanα=sinα/cosα=-4/3
cosα=〔1-tan^(α/2)〕/[1+tan^(α/2)〕
=[1-16/9]/[1+16/9]
=-7/25
2sin^2α-sinαcosα-3cos^2α
=(2sinα-3cosα)(sinα+cosα)
=(2cosαtanα-3cosα)(cosαtanα+cosα)
=(cosα)^...
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tanα=sinα/cosα=-4/3
cosα=〔1-tan^(α/2)〕/[1+tan^(α/2)〕
=[1-16/9]/[1+16/9]
=-7/25
2sin^2α-sinαcosα-3cos^2α
=(2sinα-3cosα)(sinα+cosα)
=(2cosαtanα-3cosα)(cosαtanα+cosα)
=(cosα)^2(2tanα-3)(tanα+1)
=(cosα)^2(-4/3*2-3)(-4/3+1)
=17/9(cosα)^2
=17/9*(-7/25)^2
=833/5625
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tanα=sinα/cosα=-4/3
将sinα=-4cosα/3
代入sin^2α+cos^2α=1
解出sinα=4/5 cosα=-3/5或sinα=-4/5 cosα=3/5
代入后面的式子就可以算出来了
2sin^2α+sinαcosα-3cos^2α
=1-cos2α+sin2α/2-(3/2+3cos2α/2)
=sin2α/2-5cos2α/2-1/2
=2tanα/[2(1+tan^2α)]-5(1-tan^2α)/[2(1+tan^2α)]-1/2
=(-4/3)/【1+(-4/3)^2】-5【1-(-4/3)^2】/【2(1+(-4/3)^2)】-1/2
=-12/25+7/10-1/2
=-7/25