5
$\begingroup$

What is the range of $ y = (\operatorname{ arccot x }) (\operatorname{ arccot{ - x }}) $. I solved this problem with right answer using AM GM inequality. But I received a lot of criticism for using AM GM inequality here on this site as it does not give sharp bounds. So is there a better way? I was thinking about Jensen's inequality but that doesn't work.

What is wrong with my solution of maximum value of $ \sin \frac {A}{2} + \sin \frac{B}{2} + \sin \frac{C}{2} $ in a triangle ABC?

The side of a triangle inscribed in a given circle subtends angles $a, b, $ and $ y$ at the center.

What is wrong with this solution of find the least value of $ \sec^6 x +\csc^6 x + \sec^6 x\csc^6 x$

$\endgroup$
  • 1
    $\begingroup$ Can you please provide some context and show what you have tried? What is more, there are some issues with your LaTeX code. Use \operatorname{arccot} instead of \arccot. $\endgroup$ – Pantelis Sopasakis May 14 '19 at 12:52
  • 1
    $\begingroup$ @PantelisSopasakis I did say I solved this problem with right answer using AM GM what more could I add? $\endgroup$ – user541396 May 14 '19 at 12:54
  • 1
    $\begingroup$ @PantelisSopasakis anything else I should add?? $\endgroup$ – user541396 May 14 '19 at 13:03
  • 1
    $\begingroup$ @PantelisSopasakis questions are put on hold even if they follow "this guide"math.meta.stackexchange.com/questions/30088/…. So I doubt how helpful it is. $\endgroup$ – user541396 May 14 '19 at 13:14
  • 2
    $\begingroup$ You're right, MSE doesn't work perfectly. I meant to say that the better you phrase your questions, the higher the chances that you'll get an answer. $\endgroup$ – Pantelis Sopasakis May 14 '19 at 13:18
4
$\begingroup$

Like How do I prove that $\arccos(x) + \arccos(-x)=\pi$ when $x \in [-1,1]$?,

arccot$(x)\cdot$arccot$(-x)=$arccot$(x)(\pi-$arccot$(x))=\left(\dfrac\pi2\right)^2-\left(\text{arccot }(x)-\dfrac\pi2\right)^2$

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.