tan(a+b)=-2,tan(a-b)=1/2,求sin2a/sin2b的值
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tan(a+b)=-2,tan(a-b)=1/2,求sin2a/sin2b的值
tan(a+b)tan(a-b)=-1
tan^2a-tan^2b=-(1-tan^2atan^2b)
tan^2a+1=tan^2b(1+tan^2a)
(tan^2a+1)(tan^2b-1)=0
tan^2b=1
tanb=1,或tanb=-1
tana+tanb=-2(1-tanatanb)
所以tana=3,或tana=-3
sin2a/sin2b=sinacosa/sinbcosb=(tana/tanb)*(cos^2a/cos^2b)
=3*(1+tan^2b)/(1+tan^2a)=3*2/10=3/5
tan^2a-tan^2b=-(1-tan^2atan^2b)
tan^2a+1=tan^2b(1+tan^2a)
(tan^2a+1)(tan^2b-1)=0
tan^2b=1
tanb=1,或tanb=-1
tana+tanb=-2(1-tanatanb)
所以tana=3,或tana=-3
sin2a/sin2b=sinacosa/sinbcosb=(tana/tanb)*(cos^2a/cos^2b)
=3*(1+tan^2b)/(1+tan^2a)=3*2/10=3/5
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