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True or False: The minimum value of n for which $\tan^{-1}\Large {\frac{n}{\pi}}\;>\Large {\frac{\pi}{4}},\normalsize\;n\in N,$ is valid is 5

$\begin{array}{1 1} \text{False, Minimum Value is 4} \\ \text{Yes Minimum Value if 5} \\ \text{False, Minimum Value is 3} \\ \text{Cannot be Determined }\end{array} $

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Toolbox:
  • \(tan\large\frac{\pi}{4}=1\)
  • if x>\(\large\frac{\pi}{4}\), then tanx >1
  • The value of \(\pi\) is 3.14 approximately.
Ans - False
we know if x>\(\large\frac{\pi}{4}\), then tanx >1 and
\(given:tan^{-1}\large\frac{n}{\pi}>\frac{\pi}{4}\)
 
\(\Rightarrow\:tan(tan^{-1}\large\frac{n}{\pi})>tan\large\frac{\pi}{4}\)
\(\Rightarrow\:tan(tan^{-1}\large\frac{n}{\pi})>1\)
\(\Rightarrow\: \large\frac{n}{\pi}>1 \Rightarrow n > \pi\)
\(\Rightarrow\:n>3.14\)
\(\Rightarrow\:\) minimum integer value of n =4

 

answered Feb 18, 2013 by thanvigandhi_1
edited Mar 19, 2013 by thanvigandhi_1
 

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