I have a problem that asks for the Taylor series of the following functions:

In both cases a is a constant

Knowing that both of these represent the formula for addition of sines, they both yield the same Taylor Series


My question regards the form of the nth term of the Taylor series, would:

(sin(a)) \frac{(-1)^nx^{2n}}{(2n)!} + (cos(a)) \frac{(-1)^nx^{2n+1}}{(2n+1)!}

be a valid way to express the nth term of the series?