已知sinb=cos(a+b)sina 证明 tanb=tana/1+2tan^2a

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sinb=cos(a+b)sina
sin(a+b-a)=cos(a+b)sina
sin(a+b)cosa-sinacos(a+b)=cos(a+b)sina
sin(a+b)cosa=2sinacos(a+b)
tan(a+b)=2tana
tanb
=tan(a+b-a)
=(tan(a+b)-tana)/(1+tan(a+b)tana)
=(2tana-tana)/(1+2tanatana)
=tana/(1+2tan²a)

已知sinA=2sinB,tanA=3tanB,求证cos^2 A=3/8 已知sina=2sinb,tana=3tanb,求cos^2a的值 a,b属于(0,π/2),满足sinB/sinA=cos(A+B).求证tan(A+B)=2tana,tanb=(sin 证明：tan(A-B)\tanA+(sinC/sinA)*(sinC/sinA)=1,求证tanA*tanB=tanC* 已知：tan(A-B)\tanA+(sinC/sinA)*(sinC/sinA)=1,求证tanA*tanB=tanC* (sinA+sinB)/(cos A +cos B) =tan (A+B)/2 怎么证明? 已知tana+tanb=2,tan(a+b)=4.则tana*tanb 证明tan(A+B) = (tanA+tanB)/(1-tanAtanB) 已知sina+sinb=1/2,cosa+cosb=1/3,求cos(a-b),tan（a+b）已知sina=2sinB,tana=3tanB,则cos=? 已知sin(2A+B)=3sinB,设tanA=x,tanB=y,记y=f(x).求证：tan(A+B)=2tanA;求已知sin(2a+b)=3sinb,设tana=x,tanb=y求证：tan﹙a+b)=2tana