Question

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 =

• A. 0
• B. xyz
• C. 3xyz
• D. $\sqrt{xyz}$

Answer 1

Answer: (B)

Put $ta{n}^{-1}x=A$
$\Rightarrow x=tanA$
$ta{n}^{-1}y=B$
$\Rightarrow y=tanB$
$ta{n}^{-1}z=C$
$\Rightarrow z=tanC$
$\therefore A+B+C=\pi$
$\therefore x+y+z=tanA+tanB+tanC$
$=tanAtanBtanC$
$=xyz$