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...