Evaluate: 2√(2) 45° 30°+2√(3) 30°

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 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 30/1/1, 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: $22 cos 4 5^{\circ} sin 3 0^{\circ} + 23 cos 3 0^{\circ}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 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 $cos 4 5^{\circ}$ , $sin 3 0^{\circ}$ and $cos 3 0^{\circ}$ .

Hint 2

The first product simplifies to 1 and the second to 3.

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 $cos 4 5^{\circ} = \frac{1}{2}$ , $sin 3 0^{\circ} = \frac{1}{2}$ and $cos 3 0^{\circ} = \frac{3}{2}$ .
$22 \times \frac{1}{2} \times \frac{1}{2} + 23 \times \frac{3}{2}$
1½ marks
$= 1 + 3 = 4$
½ mark

Answer: 4

Where the marks are

Substitutes the correct values of $cos 4 5^{\circ}$ , $sin 3 0^{\circ}$ and $cos 3 0^{\circ}$ (½ mark each, 1½ marks)
Simplifies to 4 (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Relationships Between Trigonometric Ratios

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 30/1/1 (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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