Evaluate : (² 60°)/(² 60°+ ² 30°)

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

CBSE Class 10 Mathematics Standard 2025: question 21(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section B, question 21(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(b) · 2 marks · Very short answerIntroduction to Trigonometry

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

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

Hints

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

Hint 1

Write down the standard values of $tan 6 0^{\circ}$ , $sin 6 0^{\circ}$ and $cos 3 0^{\circ}$ .

Hint 2

Square each value, add the two in the denominator, then divide.

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 the standard values $tan 6 0^{\circ} = 3$ , $sin 6 0^{\circ} = \frac{3}{2}$ and $cos 3 0^{\circ} = \frac{3}{2}$ :
$\frac{( 3 ) ^{2}}{( \frac{3}{2} ) ^{2} + ( \frac{3}{2} ) ^{2}} = \frac{3}{\frac{3}{4} + \frac{3}{4}} = \frac{3}{\frac{3}{2}}$
1½ marks
$= 2$
½ mark

Answer: 2

Where the marks are

Substitutes correct values of $tan 6 0^{\circ}$ , $sin 6 0^{\circ}$ , $cos 3 0^{\circ}$ (1½ marks)
Simplifies to 2 (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 paper2025 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 21(b)

Hints

Step-by-step solution

Revise the chapter

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