Define function f_{k}(x) (where k is a positive integer) as follows:
f_{k}(x)=(\cos k x)(\cos x)^{k}+(\sin k x)(\sin x)^{k}-(\cos 2 x)^{k}
Find the sum of all distinct value(s) of k such that f_{k}(x) is a constant function.
Define function f_{k}(x) (where k is a positive integer) as follows:
Find the sum of all distinct value(s) of k such that f_{k}(x) is a constant function.