若锐角a、b满足cosa=4/5，cos（a-b）=4/5，求sinb

cosa=cos(a-b)
因为锐角a、b
0<a<π/2 0<b<π/2
-π/2<-b<0 -π/2<a-b<π/2
所以a=a-b或a=-(a-b)
a=a-b b=0 与锐角b矛盾
a=-(a-b) b=2a
a-b<0
sin(a-b)=-√(1-(cos(a-b)^2))=-3/5
sina=√(1-(cosa^2))=3/5

cosb
=cos(a-(a-b))
=cosa*cos(a-b)+sinasin(a-b)
=4/5*4/5+3/5*(-3/5)
=7/25

sinb=√(1-(sinb)^2)=24/25

sinb=sin[a-(a-b)]=sinacos(a-b)-sin(a-b)cosa

24/25

0<b<π/2
所以-π/2<-b<0
0<a<π/2
所以-π/2<a-b<π/2

cosa=cos(±a)=cos(a-b)
所以a=a-b或-a=a-b
a=a-b,b=0,不符合b是锐角
-a=a-b
b=2a

cosa=4/5
(sina)^2+(cosa)^2=1
a是锐角，所以sina>0
sina=3/5

sinb=sin2a=sin(a+a)=sinacosa+cosasina=2sinacosa=24/25