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)+cos^2(45-x)
=asinxcosx-(cosx)^2+(cos45cosx+sin45sinx)^2
=asinxcosx-(cosx)^2+[(cosx)^2+(sinx)^2+2sinxcos]/2
=(a+1)sinxcosx-[(cosx)^2-(sinx)^2]/2
=(a+1)(sin2x)/2-(cos2x)/2
f(-60)=-√3(a+1)/4+1/4
f(0)=-1/2
f(-60)=f(0)
-√3(a+1)/4+1/4=-1/2
a+1=√3
a=√3-1
f(x)=√3(sin2x)/2-(cos2x)/2
f(x)=sin(2x-π/6)
f(x)在(kπ-π/6,kπ+π/3]上单增
f(x)在(kπ+π/3,kπ+5π/6]上单减
在[π∕4.11π∕24]里
f(π/4)=√3/2
f(π/3)=1
f(11π/24)=√2/2

周期函数啊