Question

Is this identity valid ?

Answer 1

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

Answer 2

@UnkleRhaukus , @.Sam. , @Callisto

Answer 3

let x=y=z=1

Answer 4

so?

Answer 5

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

Answer 6

@amistre64 , @experimentX

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

yep

Answer 14

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

Answer 15

i mean x,y ,z

Answer 16

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

Answer 17

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

Answer 18

lol .. that's correct!!

Answer 19

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

Answer 20

yw :)

Answer 21

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.

Answer 22

@AravindG

Answer 23

k thx