Question

1+sinθ+cosθ/1-sinθ-cosθ=1/2,则tanθ=?

Answer 1

1+sinθ+cosθ/1-sinθ-cosθ=1/2
2+2sinθ+2cosθ=1-sinθ-cosθ
3(sinθ+cosθ)=-1
9(1+sin2θ)=1
解得.sin2θ=-8/9
则,cos2θ=±√17/9
tanθ=(1-cos2θ)/sin2θ=-(9±√17)/8