TELL ME THE ANSWER FOR 15th QUESTION . PLEASE TELL ME FAST
Q15. Prove that ( cos )n = cos , for all n N by using PMI.
de Moivre's theorem by mathematical induction for natural numbers, and extending it to all integers. For an integer n, call the following statement S(n):
- For n > 0, by mathematical induction S(1) is clearly true. For our hypothesis, we assume S(k) is true for some natural k. We assume now
, considering S(k + 1):
- Now, S(k) implies S(k + 1). Through the principle of mathematical induction, it follows that the result is true for all natural numbers.
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