f(x)=1/2sin2xsinψ+COS²xcosψ-1/2sin(π/2+ψ),(0
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f(x)=1/2sin2xsinψ+COS²xcosψ-1/2sin(π/2+ψ),(0
f(x)=1/2sin2xsinψ+COS²xcosψ-1/2sin(π/2+ψ),(0<ψ<π)其图像过点(π/6,1/2)求ψ
f(x)=1/2sin2xsinψ+COS²xcosψ-1/2sin(π/2+ψ),(0
f(π/6)=√3/4sinψ+3/4cosψ-1/2cosψ
=√3/4sinψ+1/4cosψ
=1/2(√3/2sinψ+1/2cosψ)
=1/2sin(ψ+π/6)
=1/2
sin(ψ+π/6)=1
ψ+π/6=2kπ+π/2
ψ=2kπ+π/3,k∈Z
cos2x=2cos²x-1, ∴cos²x=(1+cos2x)/2
sin(π/2+£)=cos£
∴f(x)=(1/2)sin2xsin£+(1+cos2x)/2×cos£-(1/2)cos£
=(1/2)sin2xsin£+(1/2)cos2xcos£+(1/2)cos£-(1/2)cos£
=(1/2)(c...
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cos2x=2cos²x-1, ∴cos²x=(1+cos2x)/2
sin(π/2+£)=cos£
∴f(x)=(1/2)sin2xsin£+(1+cos2x)/2×cos£-(1/2)cos£
=(1/2)sin2xsin£+(1/2)cos2xcos£+(1/2)cos£-(1/2)cos£
=(1/2)(cos2xcos£+sin2xsin£)=(1/2)cos(2x-£)
x=π/6时,f(x)取得最大值, ∴cos(π/3-£)=1
0<£<π, -2π/3<π/3-£<π/3, ∴π/3-£=0
解得 £=π/3
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