If ( A + A)(1 - A) = k A, then find the value of k.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 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 430/3/1, 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

If $(sec A + tan A) (1 - sin A) = k cos A$ , then find the value of k.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

Write sec A and tan A as fractions with denominator cos A.

Hint 2

$(1 + sin A) (1 - sin A)$ is a difference of squares. Which identity does it give?

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.

$(\frac{1}{cos A} + \frac{sin A}{cos A}) (1 - sin A) = k cos A \Rightarrow \frac{( 1 + sin A ) ( 1 - sin A )}{cos A} = k cos A$
½ mark
$1 - sin^{2} A = k cos^{2} A$
½ mark
$cos^{2} A = k cos^{2} A$ [since $1 - sin^{2} A = cos^{2} A$ ]
½ mark
$k = 1$
½ mark

Answer: k = 1

Where the marks are

Writes sec A and tan A in terms of sin A and cos A (½ mark)
Simplifies to $1 - sin^{2} A = k cos^{2} A$ (½ mark)
Uses the identity to get $cos^{2} A = k cos^{2} A$ (½ mark)
Concludes k = 1 (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Proving Simple Trigonometric Identities

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 430/3/1 (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.

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

Hints

Step-by-step solution

Revise the chapter

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