Question

已知sin(θ+kπ)=-2cos(θ+kπ),k∈Z,求下列各式的值

1、tanθ 2、1+2sinθ*cosθ/sin²θ-cos²θ 3、sin²+2sinθ*cosθ+2

Answer 1

解：1、∵sin(θ+kπ)=-2cos(θ+kπ),k∈Z
则sin(θ+kπ)/cos(θ+kπ)=-2,k∈Z
∴tan(θ+kπ)=-2,k∈Z
∴tanθ=-2
2、原式=1+2sinθ*cosθ/(sin²θ-cos²θ)
=1+sin2θ/(-cos2θ)
=1-tan2θ
=1-2tanθ/(1-tan²θ)
=1-2×(-2)/[1-(-2)²]
=-1/3
3、原式=sin²θ+2sinθ*cosθ+2
=sinθ*cosθ*(tanθ+2)+2
=sinθ*cosθ*(-2+2)+2
=2
=sinθ*()