Assertion (A): Value of the expression ^-1 ((√(3))/(2) )+^-11-^-1(√(2)) is (π)/(4). Reason (R): Principal value branch of ^-1x is [-(π)/(2),(π)/(2) ] and that of ^-1x is [0,π]- \(π)/(2) \. (A) Both (A) and (R) are true and (R) is the correct explanation of (A). (B) Both (A) and (R) are true but (R) is not the correct explanation of (A). (C) (A) is true but (R) is false. (D) (A) is false but (R) is true.

MathsCBSE Class 12 · Sample paper, session 2025-26 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics sample paper 2025-26: question 19

From the official CBSE sample question paper for 2025-26, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedInverse Trigonometric Functions

Assertion (A): Value of the expression $sin^{- 1} (\frac{3}{2}) + tan^{- 1} 1 - sec^{- 1} (2)$ is $\frac{π}{4}$ .

Reason (R): Principal value branch of $sin^{- 1} x$ is $[- \frac{π}{2}, \frac{π}{2}]$ and that of $sec^{- 1} x$ is $[0, π] - {\frac{π}{2}}$ .

(A)Both (A) and (R) are true and (R) is the correct explanation of (A).
(B)Both (A) and (R) are true but (R) is not the correct explanation of (A).
(C)(A) is true but (R) is false.
(D)(A) is false but (R) is true.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

Open one hint at a time and try again before the next.

Hint 1

Find each principal value separately.

Hint 2

Do $tan^{- 1} 1$ and $sec^{- 1} 2$ cancel each other?

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$sin^{- 1} \frac{3}{2} + tan^{- 1} 1 - sec^{- 1} 2 = \frac{π}{3} + \frac{π}{4} - \frac{π}{4} = \frac{π}{3} \neq = \frac{π}{4}$ , so (A) is false.
The principal value branches stated in (R) are correct, so (R) is true. Option (D).
1 mark

Answer: Option (D)

Where the marks are

Evaluates the expression as $\frac{π}{3}$ and confirms that (R) is correct (1 mark)

Revise the chapter

Chapter: Inverse Trigonometric Functions (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Inverse Trigonometric Functions, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Mathematics sample paper 2025-26: question 19

Hints

Step-by-step solution

Revise the chapter

More questions from Inverse Trigonometric Functions