已知tanα=-2求(3sinα-2cosα)/(5sinα+4cosα)求sin^2α+2sinαcosα-3cos^2α
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已知tanα=-2求(3sinα-2cosα)/(5sinα+4cosα)求sin^2α+2sinαcosα-3cos^2α
已知tanα=-2求(3sinα-2cosα)/(5sinα+4cosα)求sin^2α+2sinαcosα-3cos^2α
已知tanα=-2求(3sinα-2cosα)/(5sinα+4cosα)求sin^2α+2sinαcosα-3cos^2α
(3sinα-2cosα)/(5sinα+4cosα)(分子分母同时除以cosα)
=(3tanα-2)/(5tanα+4)
=(-2*3-2)/(-2*5+4)
=-8/(-6)
=4/3
sin^2α+2sinαcosα-3cos^2α
=cos^2α*[sin^2α/cos^2α+2sinαcosα/cos^2α-3cos^2α/cos^2α]
=cos^2α*[tan^2α+2tanα-3]
=cos^2α*(tanα+3)(tanα-1)
=(1+cos2α)/2*(-2+3)(-2-1)
=-3/2-3cos2α/2
=-3/2-3/2*[(1-tan^2α)/(1+tan^2α)]
=-3/2-3/2*[(1-4)/(1+4)]
=-3/2+3/2*3/5
=-3/2+9/10
=-15/10+9/10
=-6/10
=-3/5
tan(a+π/4)=2
tanπ/4=1
所以tan(a+π/4)=(tana+1)/(1-tana)=2
tana+1=2-2tana
tana=1/3
所以sina/cosa=1/3
cosa=sina/3
(sina)^2+(cosa)^2=1
所以(sina)^2=9/10
tan2a=2tana/(1-tan^2a...
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tan(a+π/4)=2
tanπ/4=1
所以tan(a+π/4)=(tana+1)/(1-tana)=2
tana+1=2-2tana
tana=1/3
所以sina/cosa=1/3
cosa=sina/3
(sina)^2+(cosa)^2=1
所以(sina)^2=9/10
tan2a=2tana/(1-tan^2a)=(2/3)/(8/9)=3/4
所以原式=1-2(sina)^2+3(sina)^2+tan2a
=1+(sina)^2+tan2a
=53/20
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