求解：arctan[f（x）]+arctan［g（x）］

解：設(shè)arctan[f（x）]=A(x),arctan［g（x）］=B（x）.

則arctan[f（x）]+arctan［g（x）］=A(x)+B(x).且f(x)=tan[A(x)],g(x)=tan[B(x)].

所以tan[A(x)+B(x)]=（tan[A(x)]+tan[B(x)]）/（1-tan［A(x)］tan[B(x)]）=(f(x)+g(x))/(1-f(x)g(x))

所以A(x)+B(x)=arctan[(f(x)+g(x))/(1-f(x)g(x))]

所以原式=arctan[(f(x)+g(x))/(1-f(x)g(x))]