Quandaries
and Queries 

hello my name is Chris, student any help would be appreciated 

Hi Chris, There are two steps in an induction argument. First you need to get started, that is you need to verify that the statement is true when n=1. n=1:
The second step is to assume that the statement is true for some value of n and then show it is true for the next value of n. I will assume that the statement is true when n=k. Assume cos(k x pi + X) = (1)^{k} cosX: Verify that the statement is true for the next value of k. That is show that cos([k+1] x pi + X) = (1)^{k+1} cosX:
Thus the statement is true when n=1, and if it is true for any value of n it is true for the next value of n. Thus the statement is true for all positive integers. Penny 

