已知f(x)=sin(x+θ/2)cos(x+θ/2)+2√3cos²(x+θ/2)-√3,且0≤θ≤π,求θ值使函数f(x)为奇函数.
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![已知f(x)=sin(x+θ/2)cos(x+θ/2)+2√3cos²(x+θ/2)-√3,且0≤θ≤π,求θ值使函数f(x)为奇函数.](/uploads/image/z/11521740-12-0.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%3Dsin%EF%BC%88x%2B%CE%B8%2F2%EF%BC%89cos%EF%BC%88x%2B%CE%B8%2F2%EF%BC%89%2B2%E2%88%9A3cos%26%23178%3B%EF%BC%88x%2B%CE%B8%2F2%EF%BC%89-%E2%88%9A3%2C%E4%B8%940%E2%89%A4%CE%B8%E2%89%A4%CF%80%2C%E6%B1%82%CE%B8%E5%80%BC%E4%BD%BF%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E4%B8%BA%E5%A5%87%E5%87%BD%E6%95%B0.)
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已知f(x)=sin(x+θ/2)cos(x+θ/2)+2√3cos²(x+θ/2)-√3,且0≤θ≤π,求θ值使函数f(x)为奇函数.
已知f(x)=sin(x+θ/2)cos(x+θ/2)+2√3cos²(x+θ/2)-√3,且0≤θ≤π,求θ值使函数f(x)
为奇函数.
已知f(x)=sin(x+θ/2)cos(x+θ/2)+2√3cos²(x+θ/2)-√3,且0≤θ≤π,求θ值使函数f(x)为奇函数.
f(x)=2sin(x+θ/2)cos(x+θ/2)+2√3cos^2(x+θ/2)-√3
=sin(2x+θ)+√3(1+cos(2x+θ))-√3
=sin(2x+θ)+√3cos(2x+θ)
=2sin(2x+θ+π/3)
f(x)是 奇函数
那么θ+π/3=kπ(k∈Z)
又0≤θ≤π
那么θ=2π/3