If (α+β)=0, then value of ((α+β)/(2) ) is equal to: (A) (1)/(√(2)) (B) 1/2 (C) 0 (D) √(2)

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 12

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section A, question 12, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q12 · 1 mark · MCQIntroduction to Trigonometry

If $cos (α + β) = 0$ , then value of $cos (\frac{α + β}{2})$ is equal to:

(A) $\frac{1}{2}$
(B) $\frac{1}{2}$
(C)0
(D) $2$

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

For which acute angle is cosine equal to 0?

Hint 2

$α + β = 9 0^{\circ}$ , so half of it is $4 5^{\circ}$ .

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.

$cos (α + β) = 0 = cos 9 0^{\circ} \Rightarrow α + β = 9 0^{\circ}$ .
So $cos (\frac{α + β}{2}) = cos 4 5^{\circ} = \frac{1}{2}$ . The answer is option (A).
1 mark

Answer: $\frac{1}{2}$ , option (A)

Where the marks are

Gets $α + β = 9 0^{\circ}$ and $cos 4 5^{\circ} = \frac{1}{2}$ , option (A) (1 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.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2024: question 12

Hints

Step-by-step solution

Revise the chapter

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