已知函数f(X)=2sin(ωx-π/6)sin(ωx+π/3) (其中ω为正常数,x∈R)的最小正周期为π (1)求ω的值(2)在△ABC中,若A<B,且f(A)=f(B)=1/2,求BC/AB
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![已知函数f(X)=2sin(ωx-π/6)sin(ωx+π/3) (其中ω为正常数,x∈R)的最小正周期为π (1)求ω的值(2)在△ABC中,若A<B,且f(A)=f(B)=1/2,求BC/AB](/uploads/image/z/4112909-53-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28X%29%3D2sin%28%CF%89x-%CF%80%2F6%29sin%28%CF%89x%2B%CF%80%2F3%29+%28%E5%85%B6%E4%B8%AD%CF%89%E4%B8%BA%E6%AD%A3%E5%B8%B8%E6%95%B0%2Cx%E2%88%88R%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E4%B8%BA%CF%80+%EF%BC%881%EF%BC%89%E6%B1%82%CF%89%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2C%E8%8B%A5A%EF%BC%9CB%2C%E4%B8%94f%28A%29%EF%BC%9Df%28B%29%EF%BC%9D1%2F2%2C%E6%B1%82BC%2FAB)
已知函数f(X)=2sin(ωx-π/6)sin(ωx+π/3) (其中ω为正常数,x∈R)的最小正周期为π (1)求ω的值(2)在△ABC中,若A<B,且f(A)=f(B)=1/2,求BC/AB
已知函数f(X)=2sin(ωx-π/6)sin(ωx+π/3) (其中ω为正常数,x∈R)的最小正周期为π
(1)求ω的值
(2)在△ABC中,若A<B,且f(A)=f(B)=1/2,求BC/AB
已知函数f(X)=2sin(ωx-π/6)sin(ωx+π/3) (其中ω为正常数,x∈R)的最小正周期为π (1)求ω的值(2)在△ABC中,若A<B,且f(A)=f(B)=1/2,求BC/AB
(1)f(X)=2sin(ωx-π/6)sin(ωx+π/3)=-【cos(2ωx+π/6)-cos(-π/2)】=-cos(2ωx+π/6)
所以最小正周期为2π/2ω=π
ω=1
(2)f(A)=f(B)=1/2
所以cos(2x+π/6)=-1/2
可以算出A,B,C
所以BC/AB=A/C
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