f(x)=cos²x+sin(2x)=(1+cos(2x))/2+sin(2x)=1/2*cos(2x)+sin(2x)+1/2=√((1/2)²+1²)sin(2x+arctan(1/2))+1/2≤√((1/2)²+1²)+1/2=(1+√5)/2最大值为(1+√5)/2