f(x)=cosx(asinx-cosx)+cos^2(π∕2-x）满足f(-60)=f(0).求在[π∕4.11π∕24]的最大值最小值

f(x)=cosx(asinx-cosx)+cos^2(π∕2-x）满足f(-60)=f(0).求在[π∕4.11π∕24]的最大值最小值
f(x)=cosx(asinx-cosx)+cos^2(π∕2-x）满足f(-60)=f(0).求在[π∕4.11π∕24]的最大值最小值

f(x)=cosx(asinx-cosx)+cos^2(π∕2-x）满足f(-60)=f(0).求在[π∕4.11π∕24]的最大值最小值
f(x)=cosx(asinx-cosx)+(sinx)^2
f(0)= -1
f(-60)=1/2(二分之根号三a--1/2)+3/4
因为f(-60)=f(0)
则a=负二倍的根号三
则:经化简f(x)= -3^1/2sin(2x)-cos(2x)= -2sin(2x+π/6)
则当x=π/4 最小值：负二分之根号三
当x=11π/24 最大值 ：sin15 没笔,不好算,自己去化简啊

f(x)=cosx(asinx-cosx)+cos^2(π/2-x)
f(0)=-1
f(-π/3)=(1/2)(-√3a/2-1/2)+3/4=-√3a/4+1/2
-√3a/4+1/2=-1
a=2√3
f(x)=cosx(2√3sinx-cosx)+cos^2(π/2-x)
=2√3sinxcosx-(cosx)^2+(sinx)^2

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f(x)=cosx(asinx-cosx)+cos^2(π/2-x)
f(0)=-1
f(-π/3)=(1/2)(-√3a/2-1/2)+3/4=-√3a/4+1/2
-√3a/4+1/2=-1
a=2√3
f(x)=cosx(2√3sinx-cosx)+cos^2(π/2-x)
=2√3sinxcosx-(cosx)^2+(sinx)^2
=√3sin(2x)-cos(2x)
=2sin(2x-π/6)
π/4≤x≤11π/24
π/2≤2x≤11π/12
π/3≤2x-π/6≤3π/4
当π/3≤2x-π/6≤π/2时，√3/2≤sin(2x-π/6)≤1
当π/2≤2x-π/6≤3π/4时，√2/2≤sin(2x-π/6)≤1
所以√2/2≤sin(2x-π/6)≤1
最大值为1，最小值为√2/2。

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