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Which of the ...

Question

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

[- \frac{π}{2}, \frac{π}{2}]

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(0, π) - {\frac{π}{2}}

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(0, π)

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[0, π]

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Solution

The correct option is D $[0, π]$
The principal value branch of ${cos}^{- 1} x$ is $[0, π]$ Therefore, option $(c)$ is correct.

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(a) [\frac{π}{2}, \frac{3 π}{2}] (b) [π, 2 π] - \{\frac{3 π}{2}\} (c) (0, π) (d) [2 π, 3 π]

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

{tan}^{- 1} x

{cos}^{- 1} x

Which of the following is the principal value branch of $c o s^{- 1} x ?$

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

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