Evaluate: ² 60°+ 2 45°- ² 30°.

MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 24

From the official CBSE sample question paper for 2023-24, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerIntroduction to Trigonometry

Evaluate: $sin^{2} 6 0^{\circ} + 2 tan 4 5^{\circ} - cos^{2} 3 0^{\circ}$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Recall the values of $sin 6 0^{\circ}$ , $tan 4 5^{\circ}$ and $cos 3 0^{\circ}$ from the standard table.

Hint 2

Notice that $sin 6 0^{\circ} = cos 3 0^{\circ}$ . What happens to their squares when one is subtracted from the other?

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 $sin 6 0^{\circ} = \frac{3}{2}$ , $tan 4 5^{\circ} = 1$ and $cos 3 0^{\circ} = \frac{3}{2}$ :
$(\frac{3}{2})^{2} + 2 (1) - (\frac{3}{2})^{2}$
1 mark
$= \frac{3}{4} + 2 - \frac{3}{4} = 2$
1 mark

Answer: 2

Where the marks are

Correct substitution of the trigonometric values (1 mark)
Simplifies to 2 (1 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 2023-24 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2023-24: question 24

Hints

Step-by-step solution

Revise the chapter

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