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Prove that 45°= 1… (Class 10 Maths Basic 2025, Q24b)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 24(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section B, question 24(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(b) · 2 marks · Very short answerIntroduction to Trigonometry

Prove that geometrically.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

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

Hint 1

Think of a right triangle in which the two acute angles are equal.

Hint 2

If both legs equal , find of an acute angle as opposite over adjacent.

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.

  1. Take right-angled at B with , so it is an isosceles right triangle. Since , [angles opposite equal sides].

    ½ mark

  2. By the angle sum property, , so .

    ½ mark

  3. In right , . Hence .

    1 mark

Answer: tan 45° = AB/BC = x/x = 1

Where the marks are

  • Takes an isosceles right triangle with equal legs (½ mark)
  • Shows that both acute angles are using the angle sum property (½ mark)
  • Computes (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Introduction to Trigonometry, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/1/1 (Basic): 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.