9. Establish the identity 1+z+z+ +z = 1 zn+1 1. (z #1) and then use it...

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9. Establish the identity 1+z+z+ +z" = 1 zn+1 1. (z #1) and then use it to derive Lagrange's trigonometric identity: 1 + cos 0 + cos 20 + + cos no = + 1 sin[(2n + 1)0/2] 2 sin(0/2) 2 (0 < 0 < 2). Suggestion: As for the first identity, write S = 1+z+z+...+z" and consider the difference S - zS. To derive the second identity, write z = eie in the first one. 9. Establish the identity 1+z+z+ +z" = 1 zn+1 1. (z #1) and then use it to derive Lagrange's trigonometric identity: 1 + cos 0 + cos 20 + + cos no = + 1 sin[(2n + 1)0/2] 2 sin(0/2) 2 (0 < 0 < 2). Suggestion: As for the first identity, write S = 1+z+z+...+z" and consider the difference S - zS. To derive the second identity, write z = eie in the first one.