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1. Prove that: 1 + cos x + cos 2x + .....cos (n - 1)x

= {1 - cos x + cos (n - 1)x - cos nx} / 2 (1 - cos x)

= 1/2 + [{sin (n - 1/2)x}/2sin (x/2)]

2. If a = cos x + i sin x, b = cos y + i sin y, c = cos z + i sin z, prove that

{(b + c) (c + a) (a + b)}/abc = 8 cos (x - y)/2 cos (y - z)/2 cos (z - x)/2