0 votes 0 votes If $\tan x=p+1$ and $\tan y=p-1$, then the value of $2 \cot (x-y)$ is $2p$ $p^2$ $(p+1)(p-1)$ $\frac{2p}{p^2-1}$ Quantitative Aptitude isi2015-dcg quantitative-aptitude trigonometry + – gatecse asked Sep 18, 2019 • recategorized Nov 14, 2019 by Lakshman Bhaiya gatecse 825 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes Answer: $\mathbf B$ Explanation: We know that: $\begin {align} \tan\mathrm{(x-y)} &= \mathrm{\frac{\tan x - \tan y}{1 + \tan x \tan y}}\\\\ &= \mathrm{\frac{p + 1 - (p -1)} {1 + (p+1)(p-1)}}\\\\ &= \mathrm{\frac{2}{1 + p^2 - 1^2}}\\\\ &= \mathrm{\frac{2}{p^2}}\end{align}$ $\therefore \cot \mathrm{(x-y)} =\mathrm{\frac{1}{\tan (x-y)}=\frac{1}{\dfrac{2}{p^2}}= \frac{p^2}{2}}$ $\therefore \mathrm{2\times\cot(x-y) \require {cancel}= \frac{p^2}{\cancel{2}}\times \cancel[red]{2} = p^2}$ $\therefore \mathbf B$ is the correct option. `JEET answered Oct 1, 2019 • edited Nov 14, 2019 by `JEET `JEET comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes tan(x-y)=tanx -tany/1+tanxtany=p+1-p+1/1-(p2-1)=2/p2; 2cot(x-y)=2/tan(x-y)=2*p2/2=p2 option B Akash Ghosh answered Sep 20, 2019 • edited Jan 6, 2020 by Akash Ghosh Akash Ghosh comment Share Follow See all 0 reply Please log in or register to add a comment.