Evaluate : (3² 30°- 6² 30°)/(² 60°)

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 23(b)

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section B, question 23(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

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

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Recall the standard values for 30° and 60° from the trigonometric table.

Hint 2

$cos^{2} 3 0^{\circ} = \frac{3}{4}$ , $csc^{2} 3 0^{\circ} = 4$ , $tan^{2} 6 0^{\circ} = 3$ ; now simplify.

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.

Use $cos 3 0^{\circ} = \frac{3}{2}$ , $csc 3 0^{\circ} = 2$ , $tan 6 0^{\circ} = 3$ : expression $= \frac{3 ( \frac{3}{2} ) ^{2} - 6 ( 2 ) ^{2}}{( 3 ) ^{2}} = \frac{\frac{9}{4} - 24}{3}$
1½ marks
$= \frac{- \frac{87}{4}}{3} = - \frac{87}{12} = - \frac{29}{4}$
½ mark

Answer: $- \frac{29}{4}$

Where the marks are

Substitutes correct values of $cos 3 0^{\circ}$ , $csc 3 0^{\circ}$ , $tan 6 0^{\circ}$ (1½ marks)
Simplifies to $- \frac{29}{4}$ (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 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 23(b)

Hints

Step-by-step solution

Revise the chapter

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