Explanation

(d)
$\because AM \geq GM$
$\Rightarrow \frac{\frac{\cos^{3}x}{\sin x} + \frac{\sin^{3}x}{\cos x}}{2} \geq \left( \frac{\cos^{3}x}{\sin x} \bullet \frac{\sin^{3}x}{\cos x} \right)^{1/2}$
$\Rightarrow \frac{\cos^{3}x}{\sin x} + \frac{\sin^{3}x}{\cos x} \geq 2\sin{x\cos{x \geq 1}}$
Hence, option (d) is correct