1. (a) For z # 1, verify the identity 1– zn+1 1+z + z² +... + z" = 1- z (b) Use part (a) and appropriate identities from complex numbers to establish Lagrange's trigonometric identity 1 sin (n + )0 1+ cos 0 + cos 20 +... + cos n0 = + 2 sin 0 for 0 < 0 < 27. (c) For n an even positive integer, establish the formula cos no = cos" 0– cos"-2 0 sin? 0+ 2 cos"-4 0 sin“ 0+...+(-1)"/2 sin" 0 4 where k is the binomial coefficient defined by п(n - 1)(п — 2)..(п — k+1) k | k!

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