Question

【高一三角函数题】已知3sin(θ)=cos(θ)-1,则tan(θ/2)的值为_______

已知3sin(θ)=cos(θ)-1,则tan(θ/2)的值为_______
标答：0或-3
求解题过程，0是怎么算的？

Answer 1

使用万能公式
3*2tan(θ/2)/(1+tan²(θ/2))=(1-tan²(θ/2))/(1+tan²(θ/2))-1
6tan(θ/2)=(1-tan²(θ/2))-(1+tan²(θ/2))
6tan(θ/2)=1-tan²(θ/2)-1-tan²(θ/2)
6tan(θ/2)=-2tan²(θ/2)
tan²(θ/2)+3tan(θ/2)=0
tan(θ/2)(tan(θ/2)+3)=0
tan(θ/2)=0 或 tan(θ/2)=-3