Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

Find all positive integral solutions of the equation $\tan^{-1}x+\cot^{-1}y=\tan^{-1}3$

$\begin{array}{1 1}(a)\;x=1,y=2&(b)\;x=0,y=1\\(c)\;x=2,y=3&(d)\;x=2,y=3\end{array}$

1 Answer

Comment
A)
Step 1:
$\tan^{-1}x+\cot^{-1}y=\tan^{-1}3$
$\tan^{-1}x+\tan^{-1}\large\frac{1}{y}$$=\tan^{-1}3$
$\tan^{-1}\bigg[\large\frac{x+1/y}{1-x.\Large\frac{1}{y}}\bigg]$
$\Rightarrow \tan^{-1}3$
$\tan\tan^{-1}\bigg[\large\frac{xy+1}{y-x}\bigg]$$=\tan\tan^{-1}3$
$\Rightarrow \large\frac{xy+1}{y-x}$$=3$
$\Rightarrow xy+1=3(y-x)$
$\Rightarrow xy+1=3y-3x$
$\Rightarrow xy-3y=-3x-1$
$\Rightarrow y[x-3]=-[3x+1]$
$y=\large\frac{-(3x+1)}{x-3}$
$y=\large\frac{3x+1}{3-x}$-----(1)
Step 2:
When $x\rightarrow +ve$ numerator is +ve.
For $y$ to be +ve denominator must be +ve.
(i.e) $3-x>0$
$x< 3\Rightarrow x=1,2$
Substituting the value of $x$ in (1) we get $y=2,7$
$\Rightarrow$ solutions are $x=1,y=2$
$\Rightarrow x=2,y=7$
Hence (a) is the correct answer.
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...