设函数f(x)=向量a*b,其中向量a=(sinx,-cosx),b=(sinx-cosx,sinx-3cosx)x∈R

f(x)=a*b
=sin x (sin x -cos x)-cos x (sin x -3cos x)
=sin^2 x-sin x cos x- sin x cos x +3cos^2 x
=1-sin 2x+2cos^2 x
=2-sin 2x+cos 2x
=2-1/√2(sin 2x cos π/4 -cos 2x sin π/4)
=2-(sin(2x-π/4))/√2
=2-(sin2(x-π/8))/√2
(1)T=2π/2
=π.
(2)由－sin x在2kπ+π/2到2kπ+3π/2上单调递增,则：
2kπ+π/2

f(x)=(sinx)^2-2sinxcosx+3(cosx)^2
=1+2(cosx)^2-2sinxcosx
=2+cos2x-sin2x
=2+(根号2)sin(2x+(3pi/4))
最小正周期=2pi/2=pi
单调递增时，
2n*pi-(pi/2)<=2x+(3pi/4)<=2n*pi+(pi/2)
n*pi-(5pi/8)<=x...