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INVERSE TRIGNOMETRIC FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINVERSE TRIGNOMETRIC FUNCTIONS1 Mark
Question
State True or False for the statement.
The minimum value of n for which $\tan^{-1}\frac{\text{n}}{\pi}>\frac{\pi}{4},\ \text{n}\in\text{N},$ is valid is 5.
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Answer

False.Solution:
$\tan^{-1}\frac{\text{n}}{\pi}>\frac{\pi}{4}$
$\Rightarrow\ \frac{\text{n}}{\pi}>\tan\frac{\pi}{4}$
$\Rightarrow\ \frac{\text{n}}{\pi}>1$
$\Rightarrow\ \text{n}>\pi$
So, the minimum value of n is 4.

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