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  4. The value of tan-1(1)+tan-1(0)+tan-1(2)+tan-1(3) is equal to

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Q. The value of $tan^{-1}\left(1\right)+tan^{-1}\left(0\right)+tan^{-1}\left(2\right)+tan^{-1}\left(3\right)$ is equal to

Inverse Trigonometric Functions

Solution:

$tan^{-1}\left(1\right)+tan^{-1}\left(0\right)+tan^{-1}\left(2\right)+tan^{-1}\left(3\right)$
$= \frac{\pi}{4} + \pi+tan^{-1}\left(\frac{2+3}{1-2\cdot3}\right)\,\,\,$ (as $2 \cdot 3 >1$)
$= \frac{5\pi }{4}+tan^{-1}\left(-1\right)$
$= \frac{5\pi }{4} - \frac{\pi }{4} = \pi$