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Is this identity valid ?

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

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Other answers:

so? wrong...nothing.......lets think again
no that's the right trick ... test for few arbitrary values.
that's how i validate things ... before doing it if it looks ugly.
i jst got to this eqn by myseslf ... so i dont knw ifthis can be generalised for all x,y,q
i didnt see such an identituy in any textbook, i only saw tan-1 x+tan-1 y
can anyone tell me if this is valid for all x,y ,z?
is this correct?\[\tan^{-1}x +\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy} \]
thats why i thought of an analogous for 3x :P
i mean x,y ,z
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
lol.....ignore' is this correct?'
lol .. that's correct!!
:P thx a lot!!!!!!!!!!!!!!!!!!!111
yw :)
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.
k thx

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