TELL ME THE ANSWER FOR 15th QUESTION . PLEASE TELL ME FAST
Q15. Prove that ( cos )n = cos , for all n N by using PMI.
Dear Student,
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.
Hope this information will clear your doubts about topic.Regards
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.