Question

已知tan(α+β)=-1,,tan(α-β)=1/2,则sin2α/sin2β的值为 A.1/3 B.-1/3 C.3 D.-3

Answer 1

解答：
tan(α+β)=-1,,tan(α-β)=1/2
则sin2α/sin2β
=sin[(α+β)+(α-β)]/sin[(α+β)-(α-β)]
=[sin(α+β)cos(α-β)+cos(α+β)sin(α-β)]/[sin(α+β)cos(α-β)-cos(α+β)sin(α-β)]
分子分母同时除以cos(α+β)cos(α-β)
=[tan(α+β)+tan(α-β)]/[tan(α+β)-tan(α-β)]
=[(-1)+(1/2)]/[(-1)-(1/2)]
=(-1/2)/(-3/2)
=1/3
选A