How to solve this equation? #arctg(x)+arctg(1/x)=pi/2#?

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Answer 1 · 2017-05-06T14:18:22

The given relation is valid for all real values of x. So it is not an equation but an identity. It can be proved as follows.

Let

#tan^-1x=theta#

#=>x=tantheta=cot(pi/2-theta)#

#=>cot^-1x=pi/2-theta#

#=>cot^-1x=pi/2-tan^-1x#

#=>tan^-1x+cot^-1x=pi/2#

#=>tan^-1x+tan^-1(1/x)=pi/2#

Proved