Question

Demonstrate:

Answer 1

\[\arctan(x)+\arctan(\frac{ 1 }{ x })=\frac{ \pi }{ 2 }\]

Answer 2

Consider: \[\tan (\theta)=x\]\[\tan( \frac{\pi}{2} - \theta)=\cot (\theta)=\frac{1}{x}\]

Answer 3

Done it thanks @Kainui

Answer 4

arctan x = theta
tan theta = x
arctan (1/x) = theta2
tan theta 2 = 1/x = 1/tan theta= cot theta

Answer 5

\[\theta = \tan^{-1}(x)\]\[\frac{\pi}{2}-\theta = \tan^{-1}(\frac{1}{x})\]
Just arctan and add up both equations.

I already had it typed out so I'll just post it anyways lol.