# Show that

• Apr 21st 2008, 09:15 AM
perash
Show that
Show that
cot^2(p/7) + cot^2(2p/7) + cot^2(3p/7) = 5.
• Apr 21st 2008, 12:41 PM
topsquark
Quote:

Originally Posted by perash
Show that
cot^2(p/7) + cot^2(2p/7) + cot^2(3p/7) = 5.

For what value(s) of p? This is not true in general.

-Dan

EDIT: Aaaah. You meant $p = \pi$.
• Apr 28th 2008, 07:07 PM
JaneBennet
See this: http://www.mathisfunforum.com/viewto...d=79371#p79371

It was proved that $\tan^2{\frac{\pi}{7}},\tan^2{\frac{2\pi}{7}},\tan^ 2{\frac{3\pi}{7}}$ are the roots of the equation $x^3-21x^2+35x-7=0$.

Hence $\cot^2{\frac{\pi}{7}},\cot^2{\frac{2\pi}{7}},\cot^ 2{\frac{3\pi}{7}}$ are the roots of the equation $\left(\frac{1}{x}\right)^3-21\left(\frac{1}{x}\right)^2+35\left(\frac{1}{x}\r ight)-7=0$, i.e. of the equation $7x^3-35x^2+21x-1=0$.