## AravindG 3 years ago Is this identity valid ?

1. AravindG

$\large \tan^{-1}x+\tan^{-1}y+\tan^{-1}z=\tan^{-1}\frac{x+y+z-xyz}{1-xy-yz-zx}$

2. AravindG

@UnkleRhaukus , @.Sam. , @Callisto

3. mukushla

let x=y=z=1

4. AravindG

so?

5. mukushla

lol.....im wrong...nothing.......lets think again

6. AravindG

@amistre64 , @experimentX

7. experimentX

no that's the right trick ... test for few arbitrary values.

8. experimentX

that's how i validate things ... before doing it if it looks ugly.

9. AravindG

i jst got to this eqn by myseslf ... so i dont knw ifthis can be generalised for all x,y,q

10. AravindG

i didnt see such an identituy in any textbook, i only saw tan-1 x+tan-1 y

11. AravindG

can anyone tell me if this is valid for all x,y ,z?

12. mukushla

is this correct?$\tan^{-1}x +\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$

13. AravindG

yep

14. AravindG

thats why i thought of an analogous for 3x :P

15. AravindG

i mean x,y ,z

16. mukushla

is this correct?$\tan^{-1}x +\tan^{-1}y+\tan^{-1}z=\tan^{-1}\frac{x+y}{1-xy}+\tan^{-1}z\\=\tan^{-1}\frac{z+\frac{x+y}{1-xy}}{1-z\frac{x+y}{1-xy}}=\tan^{-1}\frac{x+y+z-xyz}{1-xy-xz-zy}$ so its valid

17. mukushla

lol.....ignore' is this correct?'

18. experimentX

lol .. that's correct!!

19. AravindG

:P thx a lot!!!!!!!!!!!!!!!!!!!111

20. mukushla

yw :)

21. siddhantsharan

Just remember that it is not valid for x belonging to R due to the domain range conditions you may need to add subtract pi. Otherwise its fine.

22. siddhantsharan

@AravindG

23. AravindG

k thx