计算：arctan1/2-arctan(-2)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/07/08 09:03:15

计算：arctan1/2-arctan(-2)
要计算过程.

令a=arctan1/2∈(0,π/2)
b=arctan(-2) ∈(-π/2,0)
tana=1/2
tanb=-2
tanatanb=-1
a-b∈(0,π)
cot(a-b)=(1+tanatanb)/(tana-tanb)
=(1-1)/(1/2+2)
=0
arctan1/2-arctan(-2) = a-b=π/2.

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