Question

若cosA=3/5,cos(A-B)=56/65,且a=52,当a>b时,求b的值

Answer 1

cosA=3/5 sinA=4/5

cos(A-B)=56/65 sin(A-B)=33/65

sinB=sin(A-(A-B))

=sinAcos(A-B)-cosAsin(A-B)

=(4/5)(56/65)-(3/5)(33/65)

=(224-99)/(5*65)

=25/65=5/13

a/sinA=b/sinB

b=asinB/sinA=52*(5/13)/(4/5)1=25