令cosx=t,-1<=t<=1cos2x=2cos^2x-1=2t^2-1sin^2 x=1-cos^2x=1-t^2所以我们只需观察2(2t^2-1)+1-t^2-4t=3t^2-4t-1=3(t-2/3)^2-7/3开口向上的抛物线显然最小值在顶点t=2/3,即x=arccos 2/3min=-7/3最大值是在离顶点最远的横坐标t=-1,x=arccos -1代入得最大值为6
