Evaluate : (^-11 - ^-1 (-1/2 ) )

MathsCBSE Class 12 · Board exam 2026, set 65/1/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2026: question 25(b)

Set in the CBSE Class 12 board exam of 2026, paper 65/1/1, section B, question 25(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(b) · 2 marks · Very short answerInverse Trigonometric Functions

Evaluate : $tan (sin^{- 1} 1 - cos^{- 1} (- \frac{1}{2}))$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 65/1/1.

Hints

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

Hint 1

Principal range of $cos^{- 1}$ is $[0, π]$ ; use $cos^{- 1} (- x) = π - cos^{- 1} x$ .

Hint 2

Subtract the two angles and evaluate tan of the result.

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.

$sin^{- 1} 1 = \frac{π}{2}$ and $cos^{- 1} (- \frac{1}{2}) = π - \frac{π}{3} = \frac{2 π}{3}$ , so the expression $= tan (\frac{π}{2} - \frac{2 π}{3})$
1 mark
$= tan (- \frac{π}{6}) = - \frac{1}{3}$
1 mark

Answer: $- \frac{1}{3}$

Where the marks are

Principal values $\frac{π}{2}$ and $\frac{2 π}{3}$ (1 mark)
Simplifies to $tan (- \frac{π}{6}) = - \frac{1}{3}$ (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 paper2026 board paper, set 65/1/1: 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 2026: question 25(b)

Hints

Step-by-step solution

Revise the chapter

More questions from Inverse Trigonometric Functions