已知偶函数f(x)=Sin(w×+f)+CoS(wx+f)(w>0,|f|

已知偶函数f(x)=Sin(w×+f)+CoS(wx+f)(w>0,|f|
已知偶函数f(x)=Sin(w×+f)+CoS(wx+f)(w>0,|f|

已知偶函数f(x)=Sin(w×+f)+CoS(wx+f)(w>0,|f|
f(x)=Sin(w×+f)+CoS(wx+f)
=√2[√2/2*sin(wx+f)+√2/2cos(wx+f)]
=√2sin(wx+f+π/4)
∵最小正周期为兀,w>0
∴2π/w=π,w=2
∴f(x)=√2sin(2x+π/4+f)
∵f(x)是偶函数,
∴f(-x)=f(x)
即sin(-2x+π/4+f)=sin(2x+π/4+f)
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-sin2xcos(π/4+f)+cos2xsin(π/4+f)=sin2xcos(π/4+f)+cos2xsin(π/4+f)
∴sin2xcos(π/4+f)=0恒成立
∵sin2x是变量
∴cos(π/4+f)=0
π/4+f=kπ+π/2,k∈Z
∴f==kπ+π/4,k∈Z