Easy Trigonometry Problem

Fun and Easy Problems from 103 trigonometry problems :)

Compute expressions below;

(a) $\cos 36 - \cos 72$
(b) $\sin 10 \sin 50 \sin 70$

The solution will be posted on Sep 4, 2009

Proof of AM-GM-HM Inequality by Geometric idea

The most simple version of AM-GM-HM Inequality is;

$a,b \in R$
$\frac{a+b}{2}\ge \sqrt{ab} \ge \frac{2ab}{a+b}$

Anyone can prove the inequality above by using Geometric ideas?

Solution will be posted on Sep 7, 2009

The Square Pyramid Puzzle

Find all the natural number (x,y) which meets following condition;

$1^2 + 2^2 + \hdots + x^2 = y^2$

You may find the trivial solution (x,y) = (1,1).
Can you prove that there are infinitely many solutions? Or if it doesn't, can you show all the possible solutions?

The Answer Will Be Posted Next Week, Sep 6, 2009.

*Hint : (mod 6)