f(x)=sin(π-x)sin(π/2-x)+cos²x
f(x)=sinxcosx+cos²x
=1/2sin2x+1/2+1/2cos2x
=1/2(sin2x+cos2x)+1/2
=√2/2sin(2x+π/4)+1/2
T=2π/2=π
答:函数f(x)的最小正周期是π 画图出来可知 x∈ [-π/8,π/8]单调递增 [π/8,3π/8]单调递减
f(x)=sin(π-x)sin(π/2-x)+cos²x
f(x)=sinxcosx+cos²x
=1/2sin2x+1/2+1/2cos2x
=1/2(sin2x+cos2x)+1/2
=√2/2sin(2x+π/4)+1/2
T=2π/2=π
答:函数f(x)的最小正周期是π 画图出来可知 x∈ [-π/8,π/8]单调递增 [π/8,3π/8]单调递减