已知0<a<90,90<b<180,且tan(a/2)=1/2,sin(a+b)=5/13.1.分别求cosa和cosb的值.2.求tan(a-b)
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已知0<a<90,90<b<180,且tan(a/2)=1/2,sin(a+b)=5/13.1.分别求cosa和cosb的值.2.求tan(a-b)
已知0<a<90,90<b<180,且tan(a/2)=1/2,sin(a+b)=5/13.1.分别求cosa和cosb的值.2.求tan(a-b)
已知0<a<90,90<b<180,且tan(a/2)=1/2,sin(a+b)=5/13.1.分别求cosa和cosb的值.2.求tan(a-b)
1) tana=2tan(a/2)/[1-(tan(a/2))^2]=1/(1-1/4)=4/3
(sina)^2+(cosa)^2=1
(tana)^2+1=1/(cosa)^2
cosa=3/5
sina=4/5
2) sin(a+b)=5/13
cos(a+b)=-√[1-(sin(a+b))^2]=-12/13
sinb=sin(a+b-a)=sin(a+b)cosa-cos(a+b)sina=5/13*3/5+12/13*4/5=63/65
cosb=-√[1-(sinb)^2]=-16/65
tanb=-63/16
tan(a-b)=(tana-tanb)/(1+tanatanb)=(4/3+63/16)/(1-4/3*63/16)=-253/204
tan(a/2)=1/2,sin(a+b)=5/13
(sina)^2+(cosa)^2=1
(tana)^2+1=1/(cosa)^2
cosa=3/5
sina=4/5
cos(a+b)=-√[1-(sin(a+b))^2]=-12/13
sinb=sin(a+b-a)=sin(a+b)cosa-cos(a+b)sina=5/13*3/5+12/13*4/5=63/65
cosb=-√[1-(sinb)^2]=-16/65
tanb=-63/16
tan(a-b)=-253/204