Consider the following in respect of inverse circular functions : I. \( \sin^{-1}(-x) = -\sin^{-1}x \) II. \( \cos^{-1}(-x) = \cos^{-1}x \) III. \( \tan^{-1}(-x) = \pi - \tan^{-1}x \) IV. \( \cot^{-1}(-x) = \pi - \cot^{-1}x \) How many of the above are correct ?
- A. One
- B. Two ✓
- C. Three
- D. All the four
Correct Answer: B. Two
Explanation
Statements I and IV are standard properties of inverse trigonometric functions. Statement II is incorrect (it should be \pi - \cos^{-1}x) and Statement III is incorrect (it should be -\tan^{-1}x). Hence, two statements are correct.