Question

已知90度＜B＜A＜135度,Cos(A-B)=12/13,Sin (A+B)=-3/5求sin2A的值.

Answer 1

cos(A－B)=12/13,sin(A－B)=5/13；sin(A＋B)=－3/5,cos(A＋B)=－4/5.sin2A=sin[(A－B)＋(A＋B)]=sin(A－B)cos(A＋B)＋cos(A－B)sin(A＋B)=(5/13)×(－4/5)＋(12/13)×(－3/5)=－56/65