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Prove that ( A + A - 1)/( A… (Class 10 Maths 2025, Q29A)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 29(A)

Set in the CBSE Class 10 board exam of 2025, paper 30/4/1, section C, question 29(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(A) · 3 marks · Short answerIntroduction to Trigonometry

Prove that

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/4/1.

Hints

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

Hint 1

The RHS has cot and cosec, so divide every term by .

Hint 2

Write the 1 in the numerator as and factorise.

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. Divide numerator and denominator by :
    LHS

    1 mark

  2. Replace 1 in the numerator by :

    1 mark

  3. ½ mark

  4. RHS. Hence proved.

    ½ mark

Answer: LHS = cosec A − cot A = RHS (proved)

Where the marks are

  • Divides by sin A to get expression in cot A and cosec A (1 mark)
  • Uses (1 mark)
  • Factorises numerator (½ mark)
  • Cancels to get RHS (½ 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 30/4/1 (Standard): 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.