Search any question & find its solution
Question:
Answered & Verified by Expert
If $\tan (x+y)=33$ and $x=\tan ^{-1} 3$, then $y$ is
Options:
Solution:
2473 Upvotes
Verified Answer
The correct answer is:
$\tan ^{-1}\left(\frac{3}{10}\right)$
We have, $\tan (x+y)=33$
$$
\begin{aligned}
&\Rightarrow \frac{\tan x+\tan y}{1-\tan x \tan y}=33 \\
&\Rightarrow \frac{3+\tan y}{1-3 \tan y}=33 \quad\left[\because x=\tan ^{-1} 3 \Rightarrow \tan x=3\right] \\
&\Rightarrow 3+\tan y=33-99 \tan y \\
&\Rightarrow 100 \tan y=30 \\
&\Rightarrow \tan y=\frac{3}{10} \\
&\Rightarrow y=\tan ^{-1} \frac{3}{10}
\end{aligned}
$$
$$
\begin{aligned}
&\Rightarrow \frac{\tan x+\tan y}{1-\tan x \tan y}=33 \\
&\Rightarrow \frac{3+\tan y}{1-3 \tan y}=33 \quad\left[\because x=\tan ^{-1} 3 \Rightarrow \tan x=3\right] \\
&\Rightarrow 3+\tan y=33-99 \tan y \\
&\Rightarrow 100 \tan y=30 \\
&\Rightarrow \tan y=\frac{3}{10} \\
&\Rightarrow y=\tan ^{-1} \frac{3}{10}
\end{aligned}
$$
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.