Taylor series (function)

Question

Please help me develop this function $f(x)= \frac{\arccos(x)}{\sin(x)+\cos(x)}$ near $0$, order $o(x^4)$. I started expanding it with derivatives, but the second one is really long and i stopped.

Answer 1

Hint: Solve the equation$$\frac\pi2-x-\frac{x^3}6=\left(1+x-\frac{x^2}2-\frac{x^3}6+\frac{x^4}{24}\right)\left(a_0+a_1x+a_2x^2+a_3x^3+a_4x^4\right).$$