Question

已知tan(a/2)=1/2,sin(a+b)=5/13,a,b属于(0,π),求cosb

Answer 1

cos(a/2)=1/{1+[tan(a/2)]^2}=2/根号5

sin(a/2)=cos(a/2)*tan(a/2)=1/根号5

sina=2*cos(a/2)*sin(a/2)=4/5

cosa=2*[cos(a/2)]^2-1=3/5

因为a+b>a 又 sin(a+b)