0\] Using A.M\[\ge G.M.\]we get \[\frac{{{\cot }^{-1}}x+(\pi -co{{t}^{-1}}x)}{2}\ge \sqrt{(co{{t}^{-1}}x)(\pi -co{{t}^{-1}}x)}\] \[\Rightarrow 0<{{\cot }^{-1}}(x)(\pi -co{{t}^{-1}}(x))\] \[\LE \LEFT( \frac{{{\cot }^{-1}}x+(\pi -co{{t}^{-1}}x)}{2} \right)=\frac{{{\pi }^{2}}}{4}\] \[\Rightarrow 0

"> 0\] Using A.M\[\ge G.M.\]we get \[\frac{{{\cot }^{-1}}x+(\pi -co{{t}^{-1}}x)}{2}\ge \sqrt{(co{{t}^{-1}}x)(\pi -co{{t}^{-1}}x)}\] \[\Rightarrow 0<{{\cot }^{-1}}(x)(\pi -co{{t}^{-1}}(x))\] \[\LE \LEFT( \frac{{{\cot }^{-1}}x+(\pi -co{{t}^{-1}}x)}{2} \right)=\frac{{{\pi }^{2}}}{4}\] \[\Rightarrow 0

">
Mobile Technologies Web Technologies Digital Marketing Creative Design Career Talk Medical General Tech Interviews Internet Of Things

Embark on a journey of knowledge! Take the quiz and earn valuable credits.

Take A Quiz

Challenge yourself and boost your learning! Start the quiz now to earn credits.

Take A Quiz

Unlock your potential! Begin the quiz, answer questions, and accumulate credits along the way.

Take A Quiz

Popular Categories

All
Interview Questions
QuestionBank
Quantitative Aptitude
Engineering
Govt Exams
Digital Marketing
Management
Interviews

The range of \[y=(co{{t}^{-1}}x)(co{{t}^{-1}}(-x))\] is

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) 1 year ago

  4   0   0   0   0 tuteeHUB earn credit +10 pts
5 Star Rating 1 Rating

[a] \[y=(co{{t}^{-1}}x)(co{{t}^{-1}}(-x))\] \[={{\cot }^{-1}}(x)(\pi -co{{t}^{-1}}(x))\] Now \[{{\cot }^{-1}}(x)\] and \[(\pi -co{{t}^{-1}}(x))>0\] Using A.M\[\ge G.M.\]we get \[\frac{{{\cot }^{-1}}x+(\pi -co{{t}^{-1}}x)}{2}\ge \sqrt{(co{{t}^{-1}}x)(\pi -co{{t}^{-1}}x)}\] \[\Rightarrow 0<{{\cot }^{-1}}(x)(\pi -co{{t}^{-1}}(x))\] \[\LE \LEFT( \frac{{{\cot }^{-1}}x+(\pi -co{{t}^{-1}}x)}{2} \right)=\frac{{{\pi }^{2}}}{4}\] \[\Rightarrow 0

Previous Next

Posted on 11 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

Take Quiz To Earn Credits!

Turn Your Knowledge into Earnings.

tuteehub_quiz

Tuteehub forum answer Answers

Post Answer

No matter what stage you're at in your education or career, TuteeHub will help you reach the next level that you're aiming for. Simply,Choose a subject/topic and get started in self-paced practice sessions to improve your knowledge and scores.

Explore Other Libraries

Blogs Tutorials Question Bank Feeds Careernews