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Class 12 Inverse Trigonometric Functions · Mcq Single Correct1 Marksdomains_and_ranges

Class 12 Maths · Inverse Trigonometric Functions · Mcq Single Correct #12

If \(y=\tan^{-1}x\), x real, which interval contains precisely its possible values?

(A) \(-1<y<1\)
(B) \(-\pi/2\le y\le\pi/2\)
(C) \(-\pi/2<y<\pi/2\)
(D) \(y\in\{-\pi/2,\pi/2\}\)

✅ Step-by-Step Solution

Final Answer: Option (C): \(-\pi/2<y<\pi/2\)

The arctangent principal range is the open interval (−π/2,π/2).

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