已知函数f(x)=sin(wx+π/6)+sin(wx-π/6)+2cos^2(wx/2),w使f(x)能在π/3处取得最大值的最_数学解答

已知函数f(x)=sin(wx+π/6)+sin(wx-π/6)+2cos^2(wx/2),w使f(x)能在π/3处取得最大值的最小正整数,求w
设△ABC的三边a,b,c满足b^2=ac,且边b所对的角O的取值集合为P,当x∈P是求f(x)值域
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人气：400 ℃　时间：2020-05-15 15:39:45

解答

f(x)=sin(wx+π/6)+sin(wx-π/6)+2cos^2(wx/2)
=2sincosπ/6+2cos^2(wx/2)
=gen3sin(wx)+cos(wx)+1
=2sin(wx+π/6)+1
πw/3+π/6=π/2
w=1