Alright guys, your answers are freaking me out. In math k and n are very commonly used to denote a constant number, not a variable. The question is poorly written, but from what we're given we have to assume they want us to solve for x.
First you need to undo the n in the denominator by multiplying both sides, giving nk = 1 + sin x
Subtract the 1, and now we have nk - 1 = sin x
For the love of whoever invented trigonometry, you can't divide by trigonometric functions, but you can undo them with their inverse operations. The answer should be arcsin(nk - 1) = x
Source: am mathematician