Minimum value of $\frac{1}{{3\,\,\sin \,\,\theta - 4\,\,\cos \,\,\theta + 7}}$ is

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Minimum value of

\frac{1}{{3\,\,\sin \,\,\theta - 4\,\,\cos \,\,\theta + 7}}

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Correct option: A

\frac{1}{{12}}

Option A,

\frac{1}{{12}}

, is correct because it is the minimum value of the given expression, which occurs when the denominator is maximized.

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