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State True or False for the statement
The minimum value of n for which \tan^{-1}\frac{n}{\pi}>\frac{\pi}{4},n\epsilon N   is valid is 5.

Answers (1)


\tan ^{-1}\frac{n}{\pi}>\frac{\pi}{4}

As , tan is an increasing function so applying tan on both side

we get,

\tan\left (\tan ^{-1}\frac{n}{\pi} \right )>\tan \frac{\pi}{4}

As, \tan\left (\tan ^{-1}\frac{n}{\pi} \right )=\frac{n}{\pi} and \tan\frac{\pi}{4}=1

so \frac{n}{\pi}>1

⇒ n > π
⇒ n > 3.14

As, n is a natural number, so least value of n is 4.

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