Inverse Trigonometric Functions

82 CBSE Class 12 Mathematics past-year questions from 4 papers, 2023 to 2026, with answers and worked solutions.

Difficulty: 18 easy · 61 moderate · 3 hard.
Most-asked subtopics: Domains, Ranges and Principal Value Branches (46), Evaluating Inverse Trigonometric Expressions (29), Properties of Inverse Trigonometric Functions (7).
Updated 19 August 2026.

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#1Domains, Ranges and Principal Value Branches
#2Domains, Ranges and Principal Value Branches
#3Domains, Ranges and Principal Value Branches
#4Domains, Ranges and Principal Value Branches
#5Domains, Ranges and Principal Value Branches
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#6Domains, Ranges and Principal Value Branches
#7Domains, Ranges and Principal Value Branches
#8Domains, Ranges and Principal Value Branches
#9Domains, Ranges and Principal Value Branches
#10Domains, Ranges and Principal Value Branches
#11Domains, Ranges and Principal Value Branches
#12Domains, Ranges and Principal Value Branches
#13Domains, Ranges and Principal Value Branches
#14Domains, Ranges and Principal Value Branches
#15Domains, Ranges and Principal Value Branches
#16Domains, Ranges and Principal Value Branches
Direction : In questions numbers 19 and 20, two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the following options :
#17Domains, Ranges and Principal Value Branches
If a function $f : X \to Y$ defined as $f(x) = y$ is one-one and onto, then we can define a unique function $g : Y \to X$ such that $g(y) = x$ , where $x \in X$ and $y = f(x)$ , $y \in Y$ . Function g is called the inverse of function f. The domain of sine function is R and function sine : $R \to R$ is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to $[-1, 1]$ such that inverse of sine function exists, i.e., $\sin^{-1} x$ is defined from $[-1, 1]$ to A. On the basis of the above information, answer the following questions :
#18Domains, Ranges and Principal Value Branches
If a function $f : X \to Y$ defined as $f(x) = y$ is one-one and onto, then we can define a unique function $g : Y \to X$ such that $g(y) = x$ , where $x \in X$ and $y = f(x)$ , $y \in Y$ . Function g is called the inverse of function f. The domain of sine function is R and function sine : $R \to R$ is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to $[-1, 1]$ such that inverse of sine function exists, i.e., $\sin^{-1} x$ is defined from $[-1, 1]$ to A. On the basis of the above information, answer the following questions :
#19Domains, Ranges and Principal Value Branches
If a function $f : X \to Y$ defined as $f(x) = y$ is one-one and onto, then we can define a unique function $g : Y \to X$ such that $g(y) = x$ , where $x \in X$ and $y = f(x)$ , $y \in Y$ . Function g is called the inverse of function f. The domain of sine function is R and function sine : $R \to R$ is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to $[-1, 1]$ such that inverse of sine function exists, i.e., $\sin^{-1} x$ is defined from $[-1, 1]$ to A. On the basis of the above information, answer the following questions :
#20Domains, Ranges and Principal Value Branches
#21Domains, Ranges and Principal Value Branches
#22Domains, Ranges and Principal Value Branches
#23Domains, Ranges and Principal Value Branches
Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d) as given below.
#24Domains, Ranges and Principal Value Branches
#25Domains, Ranges and Principal Value Branches
Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d) as given below.
#26Domains, Ranges and Principal Value Branches
#27Domains, Ranges and Principal Value Branches
In the following questions 19 & 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices :
#28Domains, Ranges and Principal Value Branches
#29Domains, Ranges and Principal Value Branches
Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d) as given below.
#30Domains, Ranges and Principal Value Branches
#31Domains, Ranges and Principal Value Branches
#32Domains, Ranges and Principal Value Branches
#33Domains, Ranges and Principal Value Branches
#34Domains, Ranges and Principal Value Branches
#35Domains, Ranges and Principal Value Branches
#36Domains, Ranges and Principal Value Branches
#37Domains, Ranges and Principal Value Branches
#38Domains, Ranges and Principal Value Branches
#39Domains, Ranges and Principal Value Branches
#40Domains, Ranges and Principal Value Branches
#41Domains, Ranges and Principal Value Branches
#42Domains, Ranges and Principal Value Branches
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
#43Domains, Ranges and Principal Value Branches
#44Domains, Ranges and Principal Value Branches
#45Domains, Ranges and Principal Value Branches
#46Domains, Ranges and Principal Value Branches
#47Evaluating Inverse Trigonometric Expressions
#48Evaluating Inverse Trigonometric Expressions
#49Evaluating Inverse Trigonometric Expressions
#50Evaluating Inverse Trigonometric Expressions

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Inverse Trigonometric Functions

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