Which of the following is the principal value branch of ${tan}^{- 1} x$

(0, π)

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[- \frac{π}{2}, \frac{π}{2}]

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(- \frac{π}{2}, \frac{π}{2})

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(- \frac{π}{2}, \frac{π}{2}) - {0}

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Solution

The correct option is C $(- \frac{π}{2}, \frac{π}{2})$
The principal value of ${tan}^{- 1} x$ is
$(- \frac{π}{2}, \frac{π}{2})$
$∵$ $tan x$ is bijective when $x \in (- \frac{π}{2}, \frac{π}{2})$

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Similar questions

(- \frac{π}{2}, \frac{π}{2}) (b) [- \frac{π}{2}, \frac{π}{2}] (c) (- \frac{π}{2}, \frac{π}{2}) - \{0\} (d) (0, π)

{cos}^{- 1} x

{cos}^{- 1} x

{s i n}^{- 1} x, {c o s}^{- 1} x, {t a n}^{- 1} x

{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

3 {t a n}^{- 1} (\frac{1}{2}) + 2 {t a n}^{- 1} (\frac{1}{5}) + {s i n}^{- 1} \frac{142}{65 \sqrt{5}}

{cosec}^{- 1} x

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