Evaluate: 2² 30° 60°+ ² 60°.

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 23(a)

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section B, question 23(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

Evaluate: $2 sin^{2} 3 0^{\circ} sec 6 0^{\circ} + tan^{2} 6 0^{\circ}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

Recall $sin 3 0^{\circ}$ , $cos 6 0^{\circ}$ and $tan 6 0^{\circ}$ ; $sec 6 0^{\circ} = 1/ cos 6 0^{\circ}$ .

Hint 2

Square first, then multiply and add.

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

Answer: 4

Where the marks are

Correct substitution of standard values (1½ marks)
Final value 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 paper2024 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 23(a)

Hints

Step-by-step solution

Revise the chapter

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