Question 38
$A$, $B$, $C$ are the angles of a triangle. Show that
$$
2\frac{\sin A}{A} + 2\frac{\sin B}{B} + 2\frac{\sin C}{C} \leq \left(\frac{1}{B} + \frac{1}{C}\right) \sin A + \left(\frac{1}{C} + \frac{1}{A}\right) \sin B + \left(\frac{1}{A} + \frac{1}{B}\right) \sin C.
$$
$$
2\frac{\sin A}{A} + 2\frac{\sin B}{B} + 2\frac{\sin C}{C} \leq \left(\frac{1}{B} + \frac{1}{C}\right) \sin A + \left(\frac{1}{C} + \frac{1}{A}\right) \sin B + \left(\frac{1}{A} + \frac{1}{B}\right) \sin C.
$$