Evaluate [^-1 ((3π)/(4) ) ].

MathsCBSE Class 12 · Board exam 2026, set 65/5/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2026: question 21

Set in the CBSE Class 12 board exam of 2026, paper 65/5/1, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerInverse Trigonometric Functions

Evaluate $sin [tan^{- 1} tan (\frac{3 π}{4})]$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 65/5/1.

Hints

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

Hint 1

$tan^{- 1} (tan θ) = θ$ only when $θ$ lies in $(- \frac{π}{2}, \frac{π}{2})$ . Does $\frac{3 π}{4}$ lie there?

Hint 2

First find the number $tan \frac{3 π}{4}$ .

Hint 3

Then find the angle in $(- \frac{π}{2}, \frac{π}{2})$ whose tangent is that number.

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.

$tan \frac{3 π}{4} = tan (π - \frac{π}{4}) = - 1$ , so the expression is $sin [tan^{- 1} (- 1)]$ .
1 mark
The principal value branch of $tan^{- 1}$ is $(- \frac{π}{2}, \frac{π}{2})$ , so $tan^{- 1} (- 1) = - \frac{π}{4}$ . The expression becomes $sin (- \frac{π}{4})$ .
½ mark
$sin (- \frac{π}{4}) = - \frac{1}{2}$
½ mark

Answer: $- \frac{1}{2}$

Where the marks are

Writes $tan \frac{3 π}{4} = - 1$ , i.e. $tan (π - \frac{π}{4})$ (1 mark)
Uses the principal branch to get $tan^{- 1} (- 1) = - \frac{π}{4}$ (½ mark)
Final value $- \frac{1}{2}$ (½ 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 65/5/1: every question, by section.

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CBSE Class 12 Mathematics 2026: question 21

Hints

Step-by-step solution

Revise the chapter

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