f(x)=4sin^2[(π+2x)/4].sinx+(cosx+sinx)(cosx-sinx)
问题描述：
f(x)=4sin^2[(π+2x)/4].sinx+(cosx+sinx)(cosx-sinx)
①求最小周期
②已知常数w>0,若函数y=f（wx）在区间[-π/2,2π/3]上是增函数,求w的取值范围
③若方程f（x）（sinx-1）+a=0有解,求实数a的取值范围
答
1,化简：f(x)=2(1-cos(π/2+x))sinx+(cosx)^2-(sinx)^2=2sinx+1T=2π2,f(wx)=2sin(wx)+1增区间[2kπ/w-π/2w,2kπ/w+π/2w] k是N.[-π/2,2π/3]这个区间必须是上述区间的子集.[2kπ/w-π/2w]=2π/3解得：w...