AravindG
  • AravindG
Is this identity valid ?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
AravindG
  • AravindG
\[\large \tan^{-1}x+\tan^{-1}y+\tan^{-1}z=\tan^{-1}\frac{x+y+z-xyz}{1-xy-yz-zx}\]
AravindG
  • AravindG
@UnkleRhaukus , @.Sam. , @Callisto
anonymous
  • anonymous
let x=y=z=1

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.