The value of cos⁡tan−1⁡(tan⁡2), is

The value of $\cos \{\tan^{- 1} (\tan 2)\},$ is

A
$1 / \sqrt{5}$
B
$- 1 / \sqrt{5}$
C
$\cos 2$
D
$- \cos 2$

Solution:

We have,

$\cos \{\tan^{- 1} (\tan 2)\}$

$= \cos \{\tan^{- 1} (\tan (2 - π))\} = \cos (2 - π) = \cos (π - 2) = - \cos$ 2

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