Search any question & find its solution
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 ?
Options:
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 $\tan ^{-1} x+\tan ^{-1} y=\pi+\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$
And if $x < 0, y < 0$ and $x y>1$, then $\tan ^{-1} x+\tan ^{-1} y=\pi+\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.