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Prove that : √(( A - 1)/( A +… (Class 10 Maths 2023, Q25b)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 25(b)

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, 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 answerIntroduction to Trigonometry

Prove that :

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

Add the two fractions; the common denominator is .

Hint 2

Which identity turns into a single square?

Hint 3

Finally write sec A and tan A in terms of sin A and cos A.

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. LHS . Taking the LCM :

    1 mark

  2. [since ]

    ½ mark

  3. RHS. Hence proved.

    ½ mark

Answer: LHS = 2 sec A / tan A = 2 cosec A = RHS (proved).

Where the marks are

  • Adds the two fractions to get (sec A − 1 + sec A + 1)/√(sec²A − 1) (1 mark)
  • Uses sec²A − 1 = tan²A to get 2 sec A / tan A (½ mark)
  • Simplifies to 2 cosec A (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 paper2023 board paper, set 30/5/1 (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.