解
f(x)=0.5cos²x-sinxcosx-0.5sin²x
=0.5(cos²x-sin²x)+sinxcosx
=0.5cos2x+0.5sin2x
=0.5siin(2x+π/4)
∴f(x)最小正周期是2π/2=π
令2x+π/4=kπ+π/2,解得x=kπ/2+π/8
∴函数的图像的对称轴方程是x=kπ/2+π/8(k∈z)
令2kπ-π/2<=2x+π/4<=2kπ+π/2
解得kπ-3π/8<=x<=kπ+π/8
∴函数单调增区间是[kπ-3π/8,kπ+π/8] (k∈z)