tanθ=2，则sin(π2+θ)−cos(π−θ)sin(π2−θ)−sin(π−θ)=_．
问题描述：
tanθ=2，则
=______． sin(
+θ)−cos(π−θ)π 2 sin(
−θ)−sin(π−θ)π 2
答
∵sin（
±θ）=cosθ，cos（π-θ）=-cosθ，sin（π-θ）=sinθπ 2
∴原式=
=cosθ+cosθ cosθ−sinθ
=2 1−
sinθ cosθ
=2 1−tanθ
=-22 1−2
故答案为：-2