Exercise 2.  Establish the following identities.

2 (e).      where  n  is an integer.  

Solution 2 (e).

Solution.   Use the Identities in  

                    

Add the two equations and simplify the result to obtain

                      

where n is an integer.

Therefore,     where  n  is an integer.  

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell