已知90度<B<A<135度,Cos(A-B)=3/5,Sin (A+B)=-5/13,求sin2A的值
问题描述:
已知90度<B<A<135度,Cos(A-B)=3/5,Sin (A+B)=-5/13,求sin2A的值
答
∵ 90°<B<A<135°∴ - A < - B < -90°,90° < A <135°∴ 0< A-B < 45°,180°< A+B < 270°∴ sin(A-B) = √[1-(3/5)²] = 4/5cos(A+B) = - √[1-(5/13)²] = - 12/13∴sin2A = sin【(A+B) + ...