AravindG
Is this identity valid ?
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AravindG
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\[\large \tan^{-1}x+\tan^{-1}y+\tan^{-1}z=\tan^{-1}\frac{x+y+z-xyz}{1-xy-yz-zx}\]
AravindG
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@UnkleRhaukus , @.Sam. , @Callisto
mukushla
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let x=y=z=1
AravindG
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so?
mukushla
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lol.....im wrong...nothing.......lets think again
AravindG
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@amistre64 , @experimentX
experimentX
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no that's the right trick ... test for few arbitrary values.
experimentX
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that's how i validate things ... before doing it if it looks ugly.
AravindG
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i jst got to this eqn by myseslf ... so i dont knw ifthis can be generalised for all x,y,q
AravindG
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i didnt see such an identituy in any textbook, i only saw tan-1 x+tan-1 y
AravindG
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can anyone tell me if this is valid for all x,y ,z?
mukushla
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is this correct?\[\tan^{-1}x +\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy} \]
AravindG
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yep
AravindG
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thats why i thought of an analogous for 3x :P
AravindG
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i mean x,y ,z
mukushla
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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
mukushla
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lol.....ignore' is this correct?'
experimentX
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lol .. that's correct!!
AravindG
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:P thx a lot!!!!!!!!!!!!!!!!!!!111
mukushla
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yw :)
siddhantsharan
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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.
siddhantsharan
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@AravindG
AravindG
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k thx