已知函数f(x)=sin(x+θ)+√3cos(x-θ)为奇函数,θ∈(0,π),求θ的值

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已知函数f(x)=sin(x+θ)+√3cos(x-θ)为奇函数,θ∈(0,π),求θ的值

f(x)=sin(x+θ)+√3cos(x-θ)
f(-x) = sin(-x+θ)+√3cos(-x-θ) = -sin(x-θ)+√3cos(x+θ)
f(x) = -f(-x)
sin(x+θ)+√3cos(x-θ) = sin(x-θ)-√3cos(x+θ)
sin(x+θ)+√3cos(x+θ) = sin(x-θ)-√3cos(x-θ)
(1/2)sin(x+θ)+(√3 /2)cos(x+θ) = (1/2)sin(x-θ) -(√3/2)cos(x-θ)
cos60sin(x+θ)+sin60cos(x+θ) = cos60sin(x-θ)-sin60cos(x-θ)
sin(x+θ+60) = sin(x-θ-60)
x + θ + 60 = k*360 + x -θ -60
θ = k*180 -60 其中k为整数
因为 θ∈(0,180) 所以
θ = 120