It is given that (A-B) = A B - A B. Use it to find the value of 15°.

15°= (√(3)-1)/(2√(2)) = (√(6)-√(2))/(4)

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 23(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section B, question 23(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(a) · 2 marks · Very short answerIntroduction to Trigonometry

It is given that $sin (A - B) = sin A cos B - cos A sin B$ . Use it to find the value of $sin 1 5^{\circ}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

Write 15° as the difference of two standard angles.

Hint 2

Use A = 45° and B = 30°, then substitute their sine and cosine values.

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.

$sin 1 5^{\circ} = sin (4 5^{\circ} - 3 0^{\circ}) = sin 4 5^{\circ} cos 3 0^{\circ} - cos 4 5^{\circ} sin 3 0^{\circ}$
½ mark
$= \frac{1}{2} \times \frac{3}{2} - \frac{1}{2} \times \frac{1}{2}$
1 mark
$= \frac{3 - 1}{2 2} = \frac{6 - 2}{4}$
½ mark

Answer: $sin 1 5^{\circ} = \frac{3 - 1}{2 2} = \frac{6 - 2}{4}$

Where the marks are

Writes $1 5^{\circ} = 4 5^{\circ} - 3 0^{\circ}$ and applies the formula (½ mark)
Substitutes the correct standard values (1 mark)
Simplifies to $\frac{3 - 1}{2 2}$ (½ mark)

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 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.

CBSE Class 10 Mathematics Standard 2025: question 23(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry