Given the function f (x) = sin (Wx + π / 6) + sin (Wx - π / 6) + 2cos ^ 2 (Wx / 2), W is the smallest positive integer that can make f (x) get the maximum value at π / 3, and W is calculated Let the three sides a, B, C of △ ABC satisfy B ^ 2 = AC, and the set of values of angle o of edge B is p, when x ∈ P is the range of F (x) Boss, help a classmate in urgent need | Math enthusiast | Mathematical art

Given the function f (x) = sin (Wx + π / 6) + sin (Wx - π / 6) + 2cos ^ 2 (Wx / 2), W is the smallest positive integer that can make f (x) get the maximum value at π / 3, and W is calculated Let the three sides a, B, C of △ ABC satisfy B ^ 2 = AC, and the set of values of angle o of edge B is p, when x ∈ P is the range of F (x) Boss, help a classmate in urgent need

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

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