若cosA=3/5,cos(A-B)=56/65,且a=52,当a>b时,求b的值
问题描述:
若cosA=3/5,cos(A-B)=56/65,且a=52,当a>b时,求b的值
答
cosA=3/5 sinA=4/5 cos(A-B)=56/65 sin(A-B)=33/65sinB=sin(A-(A-B))=sinAcos(A-B)-cosAsin(A-B)=(4/5)(56/65)-(3/5)(33/65)=(224-99)/(5*65)=25/65=5/13a/sinA=b/sinBb=asinB/sinA=52*(5/13)/(4/5)1=25