函数fx=2asin눀x-2√3asinxcosx+a+b,x属于(0,π/2)值域[-5,1],求a,b

2025-05-14 13:35:44
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回答1:

2sin^2x=1-cos2x
2sinxcosx=sin2x
f(x)=a-acos2x-a√3sin2x+a+b
=2a+b-2a(cos2xcosπ/3+sin2xsinπ/3)
=2a+b-2acos(2x-π/3)
-5<=f(x)<=1
显然,a≠0
a>0时,2a+b+a√3=1
2a+b-2a=-5
b=-5,a=6/(2+√3)=6(2-√3)
a<0时,2a+b-2a=1
2a+b+a√3=-5
b=1,a=-6(2+√3)=-6(2-√3)