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Question: Answered & Verified by Expert
If $x$ and $y$ are positive and $x y>1$, then what is $\tan ^{-1} x+$ $\tan ^{-1} y$ equal to ?
MathematicsInverse Trigonometric FunctionsNDANDA 2014 (Phase 1)
Options:
  • A $\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$
  • B $\pi+\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$
  • C $\pi-\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$
  • D $\tan ^{-1}\left(\frac{x-y}{1+x y}\right)$
Solution:
2648 Upvotes Verified Answer
The correct answer is: $\pi+\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$
$\tan ^{-1} \mathrm{x}+\tan ^{-1} \mathrm{y}=\tan ^{-1}\left[\frac{\mathrm{x}+\mathrm{y}}{1-\mathrm{xy}}\right]$, when $\mathrm{xy} < 1$.
And if $x < 0, y < 0$ and $x y>1$, then $\tan ^{-1} x+\tan ^{-1} y=\pi+\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$

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