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  4. The principal value of tan-1 (cot (43π/4)) is :

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Q. The principal value of $tan^{-1} \left(cot \frac{43\pi}{4}\right)$ is :

JEE MainJEE Main 2014Inverse Trigonometric Functions

Solution:

$ \tan ^{-1}[\cot (11 \pi-\pi / 4)] $
$= \tan ^{-1}[-\cot \pi / 4] $
$=-\tan ^{-1}(\cot \pi / 4) $
$=-\tan ^{-1}(1) $
$=-\pi / 4$