已知函数f（x）=sin（x+a）+(3^1/2)*cos(x-a)是偶函数,求a的值?

f(x) = f(-x)
sin（x+a）+(3^1/2)*cos(x-a) = sin（a-x）+(3^1/2)*cos(x+a)
sin（x+a）- sin（a-x）= (3^1/2)*cos(x+a) -(3^1/2)*cos(a-x)
sinx*cosa + cosx*sina - (sinacosx - cosa*sinx) = √3[cosx*cosa - sinx*sina - (cosa*cosx + sinx*sina)]
2sinx*cosa = -2√3sinx*sina
若使对任意x上面方程都成立,则
cosa = -√3sina
cota = -√3
a = kπ - π/6
k 为整数