SOLUTION: Use De Moivre's Theorem to find an expression for cot3(theta).

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Question 1181682: Use De Moivre's Theorem to find an expression for cot3(theta).
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
De Moivre's theorem: %28cos%28x%29+%2B+i%2Asin%28x%29%29%5En+=+cos%28n%2Ax%29+%2B+i%2Asin%28n%2Ax%29 for any real number x and integer n.
===> %28cos%28x%29+%2B+i%2Asin%28x%29%29%5E3+=+cos%283%2Ax%29+%2B+i%2Asin%283%2Ax%29

Expanding the left side of the preceding equation, we get

after rearranging and combining like terms.

===> cos%5E3%28x%29+-3cosx%2Asin%5E2%28x%29+=+cos%283x%29 and 3cos%5E2%28x%29%2Asinx+-+sin%5E3%28x%29+=+sin%283x%29

after equating corresponding real and imaginary parts.

Therefore,