Taylor coefficients of a function

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I'm having some trouble trying to prove the following:

Prove that in the Taylor Polynomial of $\:f(x,y)= \sin(xy)$, centered in $(0,0)$ just the coefficients of order $4k-2$ are nonzero, for $k \in\{1,2,..n\}$

I don't think induction is a good idea, can you give me some ideas?