已知函数f(x)=cos^2(x+π/3)-0.5,g(x)=1/2sin(2x+2π/3),求h(x)=f(x)-g(x)的最大

已知函数f(x)=cos^2(x+π/3)-0.5,g(x)=1/2sin(2x+2π/3),求h(x)=f(x)-g(x)的最大
已知函数f(x)=cos^2(x+π/3)-0.5,g(x)=1/2sin(2x+2π/3),求h(x)=f(x)-g(x)的最大

已知函数f(x)=cos^2(x+π/3)-0.5,g(x)=1/2sin(2x+2π/3),求h(x)=f(x)-g(x)的最大
h(x)=f(x)-g(x)
=cos^2(x+π/3)-0.5-1/2sin(2x+2π/3)
=0.5(2cos^2(x+π/3)-1)-1/2sin(2x+2π/3)
=1/2cos(2x+2π/3)-1/2sin(2x+2π/3)
= √2/2[√2/2cos(2x+2π/3)-√2/2sin(2x+2π/3)]
=√2/2[cosπ/4cos(2x+2π/3)-sinπ/4sin(2x+2π/3)]
=√2/2cos(2x+π/4+2π/3)
=√2/2cos(2x+11π/12)
所以
函数最大值为√2/2,最小值为-√2/2