Question

已知函数f(x)=2sin^2 (π/4+x)－根号下3倍cos2x，

已知函数f(x)=2sin^2 (π/4+x)－根号下3倍cos2x，。若不等式f(x)－m=2在π/4≤x≤π/2上有解，求实数m的 范围

Answer 1

f(x)=2sin^2 (π/4+x)－根号下3倍cos2x
=2sin^2 (π/4+x)-1-√3*cos2x+1
=-(1-2sin^2 (π/4+x))-√3*cos2x+1
=-cos2(π/4+x)-√3*cos2x+1
=-cos(π/2+2x)-√3*cos2x+1
=sin2x-√3*cos2x+1
=2(1/2sin2x-√3/2*cos2x)+1
=2sin(2x-π/3)+1

f(x)－m=2 m=2sin(2x-π/3)-1
sin在π/4≤x≤π/2上单调递增且为正
所以m在π/4取最小值，在π/2取最大值，带进去求出m的值即可