Atan(6/10)+Atan(1/4)=Pi/4

Question

Came across the identity, interested in the same observation from others and how have others arrive at it:

$$\arctan(6/10)+\arctan(1/4) = \frac{\pi}4$$

thank you in advance. Probably trivial. I took the long way home.

Answer 1

Using $$\tan^{-1} x+\tan^{-1} y =\tan^{-1} (\frac{x+y}{1-xy})\cdots (\text{ for }xy\not= 1)$$ ( for reference link click below)

[Reference link](Refer to:https://en.m.wikipedia.org/wiki/Inverse_trigonometric_functions)

Try it urself or see answer below

$$\tan^{-1}(\frac{6}{10}) +\tan^{-1} (\frac{1}{4})$$$$\tan^{-1}(\frac{\frac{3}{5}+\frac{1}{4}}{1-\frac{3}{5}\frac{1}{4}})$$$$\tan^{-1}(\frac{3×4+5}{4×5-3})$$$$\tan^{-1}(\frac{17}{17})$$$$\tan^{-1}(1)$$$$\frac{π}{4}$$