计算:arctan(1-x)+arctan(1+x)的值

分类: 作业答案 • 2022-01-24 10:46:24

问题描述：

答

tan(A+B) = (tanA+tanB)/(1-tanAtanB)
tan(arctan(1-x)+arctan(1+x))
= (1-x+1+x)/(1-(1-x)(1+x))
= 2/x^2
arctan(1-x)+arctan(1+x)
= arctan(2/x^2)