If {cot ^{ - 1}}frac{n}{pi } frac{pi }{6},, | vedclass

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(C) Given the inequality: ${\cot ^{ - 1}}\frac{n}{\pi } > \frac{\pi }{6}$.Since the function $f(x) = {\cot ^{ - 1}}x$ is a strictly decreasing functio

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$5$

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(C) Given the inequality: ${\cot ^{ - 1}}\frac{n}{\pi } > \frac{\pi }{6}$.Since the function $f(x) = {\cot ^{ - 1}}x$ is a strictly decreasing function,the inequality sign reverses when we take the cotangent of both sides:$\frac{n}{\pi } We know that $\cot \left( \frac{\pi }{6} \right) = \sqrt{3}$.So,$\frac{n}{\pi } Multiplying both sides by $\pi$:$n Using the approximation $\pi \approx 3.14159$ and $\sqrt{3} \approx 1.732$:$n Since $n \in N$ (natural numbers),the maximum integer value of $n$ satisfying $n < 5.44$ is $5$.

If ${\cot ^{ - 1}}\frac{n}{\pi } > \frac{\pi }{6},\,\,n \in N$,then the maximum value of $n$ is

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