Question

已知3sinθ=cosθ-1,则tanθ/2的值是

Answer 1

3sin(θ)=cos(θ)-1

6sin(θ/2)cos(θ/2)=1-2sin²(θ/2)cos(θ/2)-1

∴ sin²(θ/2)+3sin(θ/2)cos(θ/2)=0

∴ sin(θ/2)*[sin(θ/2)+3cos(θ/2)]=0

∴ sin(θ/2)=0或sin(θ/2)+3cos(θ/2)=0

∴ tan(θ/2)=sin(θ/2)/cos(θ/2)

∴ tan(θ/2)=0或tan(θ/2)=-3