Evaluate: (³ 60°- 30°)/(² 45°)

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 24(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, 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

Evaluate: $\frac{s i n ^{3} 6 0 ^{\circ} - t a n 3 0 ^{\circ}}{c o s ^{2} 4 5 ^{\circ}}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Recall the values of $sin 6 0^{\circ}$ , $tan 3 0^{\circ}$ and $cos 4 5^{\circ}$ .

Hint 2

$(\frac{3}{2})^{3} = \frac{3 3}{8}$ ; write $\frac{1}{3}$ as $\frac{3}{3}$ and take an LCM.

Hint 3

Dividing by $\frac{1}{2}$ is the same as multiplying by 2.

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.

Substitute $sin 6 0^{\circ} = \frac{3}{2}$ , $tan 3 0^{\circ} = \frac{1}{3}$ , $cos 4 5^{\circ} = \frac{1}{2}$ :
$\frac{( \frac{3}{2} ) ^{3} - \frac{1}{3}}{( \frac{1}{2} ) ^{2}} = \frac{\frac{3 3}{8} - \frac{3}{3}}{\frac{1}{2}} = \frac{\frac{9 3 - 8 3}{24}}{\frac{1}{2}}$
1½ marks
$= \frac{3}{24} \times 2 = \frac{3}{12} (= \frac{1}{4 3})$
½ mark

Answer: $\frac{3}{12}$ (or $\frac{1}{4 3}$ )

Where the marks are

Correct substitution of the standard values and simplification of the numerator (1½ marks)
Final value $\frac{3}{12}$ (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)

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 paper2026 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 2026: question 24(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry