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AravindG

Is this identity valid ?

  • one year ago
  • one year ago

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

    • one year ago
  2. AravindG
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    @UnkleRhaukus , @.Sam. , @Callisto

    • one year ago
  3. mukushla
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    let x=y=z=1

    • one year ago
  4. AravindG
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    so?

    • one year ago
  5. mukushla
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    lol.....im wrong...nothing.......lets think again

    • one year ago
  6. AravindG
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    @amistre64 , @experimentX

    • one year ago
  7. experimentX
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    no that's the right trick ... test for few arbitrary values.

    • one year ago
  8. experimentX
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    that's how i validate things ... before doing it if it looks ugly.

    • one year ago
  9. 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

    • one year ago
  10. AravindG
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    i didnt see such an identituy in any textbook, i only saw tan-1 x+tan-1 y

    • one year ago
  11. AravindG
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    can anyone tell me if this is valid for all x,y ,z?

    • one year ago
  12. mukushla
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    is this correct?\[\tan^{-1}x +\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy} \]

    • one year ago
  13. AravindG
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    yep

    • one year ago
  14. AravindG
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    thats why i thought of an analogous for 3x :P

    • one year ago
  15. AravindG
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    i mean x,y ,z

    • one year ago
  16. 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

    • one year ago
  17. mukushla
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    lol.....ignore' is this correct?'

    • one year ago
  18. experimentX
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    lol .. that's correct!!

    • one year ago
  19. AravindG
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    :P thx a lot!!!!!!!!!!!!!!!!!!!111

    • one year ago
  20. mukushla
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    yw :)

    • one year ago
  21. 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.

    • one year ago
  22. siddhantsharan
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    @AravindG

    • one year ago
  23. AravindG
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    k thx

    • one year ago
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