If 3A = 1, then find the value of 2A - ² 45°.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 2 marks · Very short answer

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

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

If $sin 3 A = 1$ , then find the value of $cos 2 A - tan^{2} 4 5^{\circ}$ .

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

For which angle is sine equal to 1?

Hint 2

Once you know A, find 2A and use the standard values of cos 60° and tan 45°.

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.

$sin 3 A = 1 = sin 9 0^{\circ} \Rightarrow 3 A = 9 0^{\circ} \Rightarrow A = 3 0^{\circ}$ .
½ mark
$cos 2 A - tan^{2} 4 5^{\circ} = cos 6 0^{\circ} - (1)^{2} = \frac{1}{2} - 1 = - \frac{1}{2}$ .
1½ marks

Answer: −1/2

Where the marks are

Gets A = 30° from sin 3A = 1 (½ mark)
Substitutes cos 60° = ½ and tan 45° = 1 to get −½ (1½ marks)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Relationships Between Trigonometric Ratios

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.

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

Hints

Step-by-step solution

Revise the chapter

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