求函數f(x)在區間[-π/4,π/4]的最大值和最小值 f(x)=sin(2x+π/3)+sin(2x-π/3)+2cos²;x-1,x∈R

求函數f(x)在區間[-π/4,π/4]的最大值和最小值 f(x)=sin(2x+π/3)+sin(2x-π/3)+2cos²;x-1,x∈R

f(x)=sin2xcos(π/3)+cos2xsin(π/3)+sin2xcos(π/3)-cos2xsin(π/3)+cos2x
=2sin2xcos(π/3)+cos2x
=sin2x+cos2x
=√2sin(2x+π/4)
f(max)=√2
f(min)= -√2