若arctan(1加x)加arctan(1减x)=4分之派,求arccos2分之x的值?急

题目

若arctan(1加x)加arctan(1减x)=4分之派,求arccos2分之x的值?急

答案

令a=arctan(1+x)
b=arctan(1-x)
tan(a+b)=1
tana=1+x,tanb=1-x
(1+x+1-x)/[1-(1-x²)]=1
2=x²
x=±√2
aeccos(x/2)
=arccos(±√2/2)
所以aeccos(x/2)=π/4或3π/4