Simplify : ^-1 (( 2x - 2x)/( 2x + 2x) ), 0 < x < (π)/(4).

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

CBSE Class 12 Mathematics 2026: question 25(a)

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

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

Simplify : $tan^{- 1} (\frac{c o s 2 x - s i n 2 x}{c o s 2 x + s i n 2 x})$ , $0 < x < \frac{π}{4}$ .

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

Divide numerator and denominator by $cos 2 x$ .

Hint 2

Recall $tan (\frac{π}{4} - θ) = \frac{1 - t a n θ}{1 + t a n θ}$ .

Hint 3

Check the angle lies in the principal range of $tan^{- 1}$ .

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.

Divide numerator and denominator by $cos 2 x$ ( $\neq = 0$ since $0 < 2 x < \frac{π}{2}$ ):
$tan^{- 1} (\frac{1 - tan 2 x}{1 + tan 2 x})$
1 mark
$= tan^{- 1} [tan (\frac{π}{4} - 2 x)] = \frac{π}{4} - 2 x$ , since $- \frac{π}{4} < \frac{π}{4} - 2 x < \frac{π}{4}$ lies in $(- \frac{π}{2}, \frac{π}{2})$ .
1 mark

Answer: $\frac{π}{4} - 2 x$

Where the marks are

Converts to $\frac{1 - t a n 2 x}{1 + t a n 2 x}$ (1 mark)
Writes as $tan (\frac{π}{4} - 2 x)$ and simplifies to $\frac{π}{4} - 2 x$ (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(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Inverse Trigonometric Functions