Question

一道高中代数题sinA+sinB=√3(cosB-cosA),a,B,∈(0,∏/2),求sin3A+sin3B的值

Answer 1

sinA+sinB=√3(cosB-cosA),两边和差化积:

2[sin(A+B)/2cos(A-B)/2]=-2√3[sin(A+B)/2sin(A-B)/2]

cos(A-B)/2=-√3sin(A-B)/2

tan[(A-B)/2]=-√3/3,∵A,B,∈(0,π/2),-π/2