Question 120
It is known that the curve $f(x) = |\sin x|$ intercepts the line $y = kx$ ($k \gt 0$) at exactly three points, the maximum $x$ coordinate of these points being $\alpha$. Prove that
$$
\frac{\cos \alpha}{\sin \alpha + \sin 3\alpha} = \frac{1 + \alpha^2}{4\alpha}.
$$
$$
\frac{\cos \alpha}{\sin \alpha + \sin 3\alpha} = \frac{1 + \alpha^2}{4\alpha}.
$$