设x1,x2是方程x²-xsinπ/5+cos4π/5=0的两根,求arctanx1+arctanx2的值RT
问题描述：
设x1,x2是方程x²-xsinπ/5+cos4π/5=0的两根,求arctanx1+arctanx2的值
RT
答
tan(arctanx1+arctanx2)=(x1+x2)/(1-x1*x2)x1+x2=sin(π/5)x1*x2=cos(4π/5)(x1+x2)/(1-x1*x2)=Sqrt[10 - 2 Sqrt[5]]/(5 + Sqrt[5])arctanx1+arctanx2=ArcTan[Sqrt[10 - 2 Sqrt[5]]/(5 + Sqrt[5])]