Question 64
Prove that
$$
\frac{\sin^{3} a}{\sin b} + \frac{\cos^{3} a}{\cos b} \geq \frac{1}{\cos(a-b)},
$$
for all $a$ and $b$ in the interval $\left(0, \frac{\pi}{2}\right)$.
$$
\frac{\sin^{3} a}{\sin b} + \frac{\cos^{3} a}{\cos b} \geq \frac{1}{\cos(a-b)},
$$
for all $a$ and $b$ in the interval $\left(0, \frac{\pi}{2}\right)$.