Question

已知a,b为锐角，cosa=4/5,tan(a-b)=-1/3,求cosb

详细点就行哦！

Answer 1

cosa=4/5,sina=3/5tana=3/4tan(a-b)=-1/3,tan(a-b)=(tana-tanb)/(1+tanatanb)=-1/3tanb=x(3/4-x)/(1+3x/4)=-1/3x=13/9tanb=13/9cosB=9√10/50

Answer 2

cosA=4/5
sinA=3/5
tanA=3/4
tan(A-B)=(tanA-tanB)/(1+tanAtanB)=(3/4-tanB)/(1+3tanB/4)=-1/3
tanB=13/9
(tanB)^2=169/81=(1-(cosB)^2)/(cosB)^2
(cosB)^2=1/(1+169/81)=81/250
由于B是锐角cosB=9/5√10=9√10/50

Answer 3

cosa=4/5, sina=3/5 tga=3/4 tg(a-b)=(tga-tgb)/(1+tgatgb)=-1/3 tgb=13/9=sinb/cosb sinb^2+cosb^2=1 cosb=9√10/50