Question

已知函数f(x)=2sin^2(π/4+x)-(根下3)cos2x-1,x属于R.设p:x属于[π/4,π/2],q属于

Answer 1

f(x)=2sin^2(π/4+x)-(√3)cos2x-1

=1-cos(π/2+2x)-(√3)cos2x-1

=sin2x-(√3)cos2x

=2sin(2x-π/3),

x∈[π/4,π/2],

2x-π/3∈[π/6,2π/3],

sin(2x-π/3∈[1/2,1],

f(x)∈[1,2],

|f(x)-m|