simplifying expressions - Evaluate trigonometric function

Can anyone help me to evaluate the trigonometric function below?
Please look that the picture for more details.

Here is the code to evaluate:

ArcTan[k] + ArcTan[1/k]

From trigonometry we know that $tan^{-1}(k)+tan^{-1}(\frac{1}{k})=\frac{\pi}{2}$ . However, when I put input that expression into Mathematica I get this:

$ArcTan[\frac{1}{k}]+ArcTan[k]$

Can anyone help me to get the result of $\frac{\pi}{2}$ ?

Answer

We know that FullSimplify[ArcTan[k] + ArcTan[1/k], k > 0] does not do it. But by first converting to exponentials, now Mathematica does it

   FullSimplify[ TrigToExp[ArcTan[k] + ArcTan[1/k]] , k > 0]

Gives as output $\frac{\pi}{2}$

Comments

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