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Q.

$\tan^{- 1} (- 2) - \tan^{- 1} (3)$ is equals to

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a

$\frac{- π}{6}$

b

$\frac{3 π}{4}$

c

$\frac{π}{6}$

d

$\frac{- 3 π}{4}$

answer is D.

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Detailed Solution

$\tan^{- 1} (- 2) - \tan^{- 1} (3) = \tan^{- 1} (\frac{(- 2) - 3}{1 + (- 2) (3)})$

$= \tan^{- 1} (\frac{- 5}{- 5}) = \tan^{- 1} (1)$

$\tan (\frac{- 3 π}{4}) = 1$

$\Rightarrow \tan^{- 1} (1) = \frac{- 3 π}{4}$

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