(1/2)已知函数f（x)=sinx+tanx,项数为27的等差数列{an}满足an属于（-90',90'),且公差d不

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(1/2)已知函数f（x)=sinx+tanx,项数为27的等差数列{an}满足an属于（-90',90'),且公差d不为零,若f(a1)+f(

f(x)=sinx+tanx
an=a1+(n-1)d
f(a1)=sina1+tana1
f(a2)=sin(a1+d)+tan(a1+d)
f(a3)=sin(a1+2d)+tan(a1+3d)
..
f(a26)=sin(a1+25d)+tan(a1+25d)
f(a27)=sin(a1+26d)+tan(a1+26d)
f(a1)+f(a27)=sina1+sin(a1+26d)+tana1+tan(a1+26d)
=2sin(a1+13d)cos13d *[1/cosa1+1/cos(a1+26d)]
f(a2)+f(26)=2sin(a1+13d)cos12d*[1/cos(a1+d)+1/cos(a1+25d)]
..
f(a13)+f(a15)=2sin(a1+13d)cosd*[1/cos(a1+12d)+1/cos(a1+14d)]
f(a14)=2sin(a1+13d)*[1+1/cos(a1+13d)]
f(a1)+f(a2)+...+f(a27)=0
sin(a1+13d)=0
f(a14)=0

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