已知函数f(x)=sin(x+π/6)+cos(x+π/3)+sinx+a(a属于R,且a为常数),若函数f(x)在[-π/2,π/2]上的最大值与最小值和为2,求实数a的值

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已知函数f(x)=sin(x+π/6)+cos(x+π/3)+sinx+a(a属于R,且a为常数),若函数f(x)在[-π/2,π/2]上的最大值与最小值和为2,求实数a的值

已知函数f(x)=sin(x+π/6)+cos(x+π/3)+sinx+a(a属于R,且a为常数),若函数f(x)在[-π/2,π/2]上的最大值与最小值和为2,求实数a的值
已知函数f(x)=sin(x+π/6)+cos(x+π/3)+sinx+a(a属于R,且a为常数),若函数f(x)在[-π/2,π/2]上的最大值
与最小值和为2,求实数a的值

已知函数f(x)=sin(x+π/6)+cos(x+π/3)+sinx+a(a属于R,且a为常数),若函数f(x)在[-π/2,π/2]上的最大值与最小值和为2,求实数a的值
f(x)=sin(x+π/6)+cos(x+π/3)+sinx+a
=sinx*cosπ/6+cosx*sinπ/6+cosx*cosπ/3-sinx*sinπ/3+sinx+a
=√3/2sinx+1/2cosx+1/2cosx-√3/2*sinx+sinx+a
=cosx+sinx+a
=√2sin(x+π/4)+a
f(x)在[-π/2,π/2]上的最大值1+a,最小值-1+a
(1+a)+(-1+a)=2
a=1