∴f(x)在R上是奇函数且是增函数;
∵f(cos2θ-2m)<-f(2msinθ-2)=f(2-2msinθ),
∴cos2θ-2m<2-2msinθ,即cos2θ-2<2m(1-sinθ),
(1)当sinθ=1时,∴-2<0恒成立,∴m∈R;
(2)当sinθ≠1即1-sinθ>0时,有2m>
cos2θ−2 |
1−sinθ |
−sin2θ−1 |
1−sinθ |
−sin2θ−1 |
1−sinθ |
−(1−sinθ)2+2(1−sinθ)−2 |
1−sinθ |
2 |
1−sinθ |
∵1−sinθ>0∴1−sinθ+
2 |
1−sinθ |
2 |
2 |
∴g(θ)≤−2
2 |
∴2m>2−2
2 |
2 |
综上有:m的取值范围是(1−
2 |