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Q.
If $ x > 0, y > 0, z > 0, xy + yz + zx < 1$ and if $\tan^{-1}x+\tan^{-1}y+\tan^{-1}z=\pi$ , then x + y + z =
Inverse Trigonometric Functions
Solution:
Put $tan^{-1}x = A $
$\Rightarrow x= tan\,A$
$ tan^{-1}y = B$
$ \Rightarrow y = tan\,B$
$ tan^{-1} z = C $
$ \Rightarrow z = tan\,C$
$\therefore A+ B + C = \pi $
$ \therefore x + y + z = tan\,A+ tan \, B + tan \, C $
$=tan\,A \,tan\,B\, tan\,C$
$ = xyz$