Min, Max

Question: (Kunihiko Chikaya 's question on facebook Trợ Giúp Toán Học)
 Let $a, b$ be constants such that $a^2-b^2>1$. Find the maximum and minimum value of $\dfrac{{\sin \,x}}{{a + b\cos x + \sin \,x}}$, and the values of $cosx, sinx$ giving the maximum and minimum value.
Answer