Evaluate the following : (3 30°- 4³ 30°)/(2² 50°+ 2² 50°)

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 24(B)

Set in the CBSE Class 10 board exam of 2025, paper 30/4/1, 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

Evaluate the following : $\frac{3 s i n 3 0 ^{\circ} - 4 s i n ^{3} 3 0 ^{\circ}}{2 s i n ^{2} 5 0 ^{\circ} + 2 c o s ^{2} 5 0 ^{\circ}}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/4/1.

Hints

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

Hint 1

Put in the value of $sin 3 0^{\circ}$ in the numerator.

Hint 2

In the denominator, take 2 common and use $sin^{2} θ + cos^{2} θ = 1$ .

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.

$= \frac{3 \times \frac{1}{2} - 4 \times \frac{1}{8}}{2 ( sin ^{2} 5 0 ^{\circ} + cos ^{2} 5 0 ^{\circ} )}$ [ $sin 3 0^{\circ} = \frac{1}{2}$ ]
1 mark
$= \frac{\frac{3}{2} - \frac{1}{2}}{2 \times 1}$ [ $sin^{2} θ + cos^{2} θ = 1$ ]
½ mark
$= \frac{1}{2}$
½ mark

Answer: $\frac{1}{2}$

Where the marks are

Substitutes $sin 3 0^{\circ} = \frac{1}{2}$ and takes 2 common in denominator (1 mark)
Uses $sin^{2} 5 0^{\circ} + cos^{2} 5 0^{\circ} = 1$ (½ mark)
Final value $\frac{1}{2}$ (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Trigonometric Ratios of an Acute Angle

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 30/4/1 (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 24(B)

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry