【题目】已知函数f(x)=sin^2(wx+π/6)-cos^2(wx+π/6),(w>0)的最小正周期为2π,(
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(1)f(x)=sin^2(wx+π/6)-cos^2(wx+π/6)
=sin^2(wx+π/6)-[1-sin^2(wx+π/6)]
=2sin^2(wx+π/6)-1
最小正周期=2π/W,所以W=1,所以f(x)=2sin^2(x+π/6)-1
(2)tanx=sinx/cosx=4/3,
(sinx)^2+(cosx)^2-1,且x∈(π,3π/2),
sinx=-4/5,cosx=-3/5,
又f(x)=2sin^2(x+π/6)-1=2(sinxcosπ/6+cosxsinπ/6)^2-1
=(7+24√3)/50
“√”根号
=sin^2(wx+π/6)-[1-sin^2(wx+π/6)]
=2sin^2(wx+π/6)-1
最小正周期=2π/W,所以W=1,所以f(x)=2sin^2(x+π/6)-1
(2)tanx=sinx/cosx=4/3,
(sinx)^2+(cosx)^2-1,且x∈(π,3π/2),
sinx=-4/5,cosx=-3/5,
又f(x)=2sin^2(x+π/6)-1=2(sinxcosπ/6+cosxsinπ/6)^2-1
=(7+24√3)/50
“√”根号
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