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Mathematics · JEE | INVERSE TRIGONOMETRIC FUNCTIONS
हिन्दीConsider the following statements regarding inverse trigonometric functions: (A) The principal value branch of \( \sin^{-1} x \) is \( [-\frac{\pi}{2}, \frac{\pi}{2}] \). (B) The domain of \( \sec^{-1} x \) is \( \mathbb{R} - (-1, 1) \). (C) \( \tan^{-1} x + \cot^{-1} x = \frac{\pi}{2} \) for all \( x \in \mathbb{R} \). (D) \( \sin^{-1}(\sin x) = x \) for all \( x \in \mathbb{R} \). Which of the above statements are correct?
View Answer & Solution
Correct answer · Option A
(A), (B) and (C) only
Explanation
Statements (A), (B), and (C) are correct definitions and identities from the principal branch table and properties. Statement (D) holds only when \( x \in [-\frac{\pi}{2}, \frac{\pi}{2}] \), hence incorrect for all \( x \in \mathbb{R} \).
