Matematické Fórum

stuart clark · 12. 06. 2011 10:31

If $\mathbf{cot^{-1}\left(\frac{y}{\sqrt{1-x^2-y^2}}\right) = 2tan^{-1}\left(\sqrt{\frac{3}{4x^2}-1}\right) - tan^{-1}\left(\sqrt{\frac{3}{x^2}-4}\right)}$

find relation between $\mathbf{x}$ and $\mathbf{y}$ .

check_drummer · 12. 06. 2011 13:21

↑ stuart clark:
Hi, by the way - where do you find inspiration for your problems - you think them up by yourself or do they come from some book or so? Thanks.

Pavel · 17. 06. 2011 13:34 — Editoval Pavel (17. 06. 2011 13:34)

↑ stuart clark:

Autor skryl část textu. Zobrazit/skrýt!

stuart clark · 19. 06. 2011 19:35

Thanks check_drummer.

@check_drummer ,taken from book

Thanks Paul, I also have a solution , but very lengthy.

anyway can you show your solution.

Thanks to all.

Pavel · 23. 06. 2011 10:34

↑ stuart clark:

Before I show my solution, I would like to clarify the definition of $\cot^{-1}x$ . There exist two concept, see Inverse cotangent and the paragraph There are at least two possible conventions for defining the inverse cotangent... Which of them is supposed in your problem? The one with the range $(-\pi/2,\pi/2)$ that is not continous at 0, or the one with the range $(0,\pi)$ that is continous anywhere in $\mathbb R$ .

Matematické Fórum

#1 12. 06. 2011 10:31

inverse (ii)

#2 12. 06. 2011 13:21

Re: inverse (ii)

#3 17. 06. 2011 13:34 — Editoval Pavel (17. 06. 2011 13:34)

Re: inverse (ii)

#4 19. 06. 2011 19:35

Re: inverse (ii)

#5 23. 06. 2011 10:34

Re: inverse (ii)