Eleven Standard >> Associate angles | Example- Integer base

Show that, for any integer n
\(\cos (n \pi + \alpha)\)=\((-1)^{n}\cos \alpha\)

Solution:
Case I

When n be an even integer
n=2m, where m is any integer

    \(\cos (n \pi + \alpha)\)
 =\(\cos (2m \pi + \alpha)\)
   In first quardent value of \(\cos\) is positive
 =+ \(\cos \alpha\)...(1) 

Case II

When n is an odd integer
n=2m+1, where m is any integer

    \(\cos (n \pi + \alpha)\)
 =\(\cos \left[(2m+1) \pi + \alpha\right]\)
   In third quardent value of \(\cos\) is positive
 =- \(\cos \alpha\)...(2) 

From (1)  and (2) we have
\(\cos (n \pi + \alpha)\)=\((-1)^{n}\cos \alpha\)
              for all \(n \in Z\)