已知f(x)=2sin^2(π/4+x)-根号3cos2x,x属于[π/4,π/2].
问题描述:
已知f(x)=2sin^2(π/4+x)-根号3cos2x,x属于[π/4,π/2].
(1)若不等|f(x)-m|
答
由题:f(x)=1-cos(π/2+2x)-√3cos2x
=1+sin2x-√3cos2x
=2sin(2x-π/6)+1
当x属于[π/4,π/2]
f(x)属于[(√6-√2)/4,√3/2]
由题:(√6-√2)/4-m>-2且√3/2-m