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Prove Equalities

The following two questions I have trouble with:

1. Show that (1- x) n-1. x = (1-x)n-1 - (1-x)n
2. Prove that if ,  are the roots of the equation t² - 2t + 2 then:

(x +) n - (x+) n / ( -) = sin n / sin n where cot  = x+1

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(See attached file for full problem description)

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Solution Summary

Equalities are proven. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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