Question

Match List I with List II

	LIST I		LIST II
A.	Range of y=cosec-1x	I.	R-(-1, 1)
B.	Domain of sec-1x	II.	(0, π)
C.	Domain of sin-1x	III.	[-1, 1]
D.	Range of y=cot-1x	IV.	\([\frac{-π}{2},\frac{π}{2}]\)-{0}

Choose the correct answer from the options given below:

• A. (A)-(I), (B)-(II), (C)-(IV), (D)-(III)
• B. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
• C. (А)-(III), (B)-(IV), (C)-(II), (D)-(I)
• D. (A)-(II), (B)-(III), (C)-(I), (D)-(IV)

Answer 1

The Correct Option is B

To match List I with List II, we need to understand the properties of inverse trigonometric functions:

A. Range of \(y = \csc^{-1} x\): The range of the cosecant inverse function is \([\frac{-\pi}{2},\frac{\pi}{2}]\) excluding 0. Therefore, this matches with IV.

B. Domain of \(\sec^{-1} x\): The domain of the secant inverse function is \(\mathbb{R} - (-1, 1)\), which matches with I.

C. Domain of \(\sin^{-1} x\): The domain of the sine inverse function is \([-1, 1]\), which matches with III.

D. Range of \(y = \cot^{-1} x\): The range of the cotangent inverse function is \((0, \pi)\), which matches with II.

Based on this analysis, the correct matching is: (A)-(IV), (B)-(I), (C)-(III), (D)-(II).