Question

已知sinA-sinB=-1/2,cosA=cosB=1/2,A,B属于(0,兀/2),求cos(A-B)的值

Answer 1

sinA-sinB=2cos((A+B)/2)sin((A-B)/2)=-1/2,cosA+cosB=2cos((A+B)/2)cos((A-B)/2)=1/2,相除得tan((A+B)/2)=-1.A-B∈(-π/2,π/2),所以(A-B)/2=-π/4,A-B=-π/2,cos(A-B)=0