If $0 < x < \frac{\pi }{2},\;$ then minimum value of $\frac{{{\rm{co}}{{\rm{s}}^3}x}}{{\sin x}} + \frac{{{{\sin }^3}x}}{{\cos x}}\;$ is

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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0 < x < \frac{\pi }{2},\;

then minimum value of

\frac{{\mathrm{co}{\mathrm{s}^3}x}}{{\sin x}} + \frac{{{{\sin }^3}x}}{{\cos x}}\;

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Correct option: D

The correct answer is D. Using AM-GM inequality, we can find that the minimum value of the expression is 1.

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