y=cos2x-2cosx,x属于[0,2π] 求函数单调区间

y=cos2x-2cosx
=2cos²x-2cosx-1
=2(cos²x-cosx+1/4)-3/2
=2(cosx-1/2)²-3/2
当cosx∈[1/2,1],y=cos2x-2cosx单调递增
单调递增区间:x∈[0,π/3]∪[5π/3,2π]
当cosx∈[-1,1/2],y=cos2x-2cosx单调递减
单调递减区间:x∈[π/3,5π/3]