设X1,X2是方程x2-xsin(π/5)+cos(π/5)=0的两根,则arctanx1+arctanx2的值是?

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设X1,X2是方程x2-xsin(π/5)+cos(π/5)=0的两根,则arctanx1+arctanx2的值是?

设X1,X2是方程x2-xsin(π/5)+cos(π/5)=0的两根,则arctanx1+arctanx2的值是?
设X1,X2是方程x2-xsin(π/5)+cos(π/5)=0的两根,则arctanx1+arctanx2的值是?

设X1,X2是方程x2-xsin(π/5)+cos(π/5)=0的两根,则arctanx1+arctanx2的值是?
两根之和是x1+x2=sin(π/5),x1x2=cos(π/5)
tan[arctanx1+arctanx2]=(x1+x2)/(1-x1x2)=sin(π/5)/[1-cos(π/5)]

X1,X2是方程x2-xsin(π/5)+cos(π/5)=0的两根
x1+x2=sin(π/5) x1x2=cos(π/5)
A=arctanx1,B=arctanx2
tanA=x1,tanB=x2
tan(A+B)
=(tanA+tanB) / (1-tanAtanB)
=(x1+x2) / (1-x1x2)
=sin(π/5)/ (1-cos(π/5))
=tan(π/10)

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