若sin(a+b)=二分之一,sin(a-b)=三分之一,则tan a/tan b为?A.5 B.-1 C.6 D1/6
问题描述：
若sin(a+b)=二分之一,sin(a-b)=三分之一,则tan a/tan b为?A.5 B.-1 C.6 D1/6
答
sin(a)cos(b)+cos(a)sin(b)=1/2; (1)
sin(a)cos(b)-cos(a)sin(b)=1/3; (2)
式(1)+(2)得：sin(a)cos(b)=5/12; (3)
式(1)-(2)得：cos(a)sin(b)=1/12; (4)
式(3)/(4)得tan a/tan b=5..答案是A