The Basic Properties of limit which are used here in this Question are :
$\lim_{x \rightarrow a} f^g = (\lim_{x \rightarrow a} f)^{(\lim_{x \rightarrow a} g)}$
$\lim_{x \rightarrow a} (f + g) = (\lim_{x \rightarrow a} f) + (\lim_{x \rightarrow a} g)$
And We can use this Trigonometric formula here : $sin x = 2 sin (\frac{x}{2})cos(\frac{x}{2})$