Consider the rhombus as illustrated where x is an unknown length, AP = AD = x , angle DAP = 36 degrees and P is a point on the diagonal AC such that PB = 1 unit.

Without using a calculator, computer or tables find the exact values of

1. $\cos 36^{o} \cos 72^{o}$
2. $\cos 36^{o} - \cos 72^{o} .$

3. Draw these two diagrams as accurately as you can and measure the lengths a and b. What do you notice? Can you prove it? (In each diagram there are two right angled triangles).