Consider the rhombus as illustrated where x is an unknown length, AP = AD = x, angle DAP = 36 ^o 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 ^ocos 72 ^o
2. cos 36 ^o - cos72 ^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).