Evaluate : 2 30° 60°- 3² 60°² 30°

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 25(A)

From the official CBSE sample question paper for 2025-26, section B, question 25(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(A) · 2 marks · Very short answerIntroduction to Trigonometry

Evaluate : $2 sin 3 0^{\circ} tan 6 0^{\circ} - 3 cos^{2} 6 0^{\circ} sec^{2} 3 0^{\circ}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

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

Hint 2

$sec 3 0^{\circ} = \frac{1}{c o s 3 0 ^{\circ}} = \frac{2}{3}$ ; square it carefully.

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 $sin 3 0^{\circ} = \frac{1}{2}, tan 6 0^{\circ} = 3, cos 6 0^{\circ} = \frac{1}{2}, sec 3 0^{\circ} = \frac{2}{3}$ : $2 (\frac{1}{2}) (3) - 3 (\frac{1}{2})^{2} (\frac{2}{3})^{2} = 3 - 3 \cdot \frac{1}{4} \cdot \frac{4}{3}$
1½ marks
$= 3 - 1$
½ mark

Answer: $3 - 1$

Where the marks are

Substitutes correct values of all four trigonometric ratios (1½ marks)
Simplifies to $3 - 1$ (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 paperSample paper 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 25(A)

Hints

Step-by-step solution

Revise the chapter

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