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Standard XII

Mathematics

Inverse Function

Which of the ...

Question

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

(- \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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(0, π)

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Solution

The correct option is A $(- \frac{π}{2}, \frac{π}{2})$
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

Q. Write the principal value branch of

{cos}^{- 1} x

Q. Inverse circular functions,Principal values of

{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

.
Using the principal values, express the following as a single angle :

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}}

Q. Which of the following corresponds to the principal value branch of tan^-1?
(a)

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

Q. Which of the following is the principal value of

{cosec}^{- 1} x

Inverse circular functions,Principal values of ${sin}^{- 1} x, {c o s}^{- 1} x, {tan}^{- 1} x$ .
${tan}^{- 1} x + {tan}^{- 1} y = {tan}^{- 1} \frac{x + y}{1 - x y}$ , $x y < 1$
$π + {tan}^{- 1} \frac{x + y}{1 - x y}$ , $x y > 1$ .
Evaluate the following :
(a) $sin [\frac{π}{3} - {sin}^{- 1} (- \frac{1}{2})]$
(b) $sin [\frac{π}{2} - {sin}^{- 1} (- \frac{\sqrt{3}}{2})]$

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Inverse Function

Standard XII Mathematics

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Which of the following is the principal value branch of tan−1x

The correct option is A (−π2,π2)The principal value of tan−1x is (−π2,π2) ∵ tanx is bijective when x∈(−π2,π2)

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

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