已知a,b为锐角,cosa=1/5,tan(a-b)=-1/3,求cosb

∵a,b为锐角
∴a-b∈(-π/2,π/2),sina>0
∵tan(a-b)=-1/3[sin(a-b)]^2+[-3sn(a-b)]^2=1
∴sin(a-b)=1/√10,con(a-b)=-3/√10
∵cosa=1/5
∴sina=√[1-(cosa)^2]=2√6/5
故cosb=cos[a-(a-b)]
=cosacos(a-b)+sinasin(a-b)
=(1/5)(-3/√10)+(2√6/5)(1/√10)
=(2√6-3)√10/50.