Range of the function f(x) = cos (K sinx) is (-1,1), then the positive integral value of K can be ______.

Obviously ksinx lies in between-k and k. 

Therefore cosine of ksinx lies in between cosk and cos0= 1. So we want cos k to be -1. So k is pi. But k is integral. So one of the possible values of k is 4.