If θ = 1, then the value of 1/2 ((θ)/(2) ) is : (A) (1)/(2√(2)) (B) (1)/(√(2)) (C) 1/2 (D) 0

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 10

Set in the CBSE Class 10 board exam of 2024, paper 30/4/1, section A, question 10, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q10 · 1 mark · MCQIntroduction to Trigonometry

If $sin θ = 1$ , then the value of $\frac{1}{2} sin (\frac{θ}{2})$ is :

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

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/4/1.

Hints

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

Hint 1

For which angle is $sin θ = 1$ ?

Hint 2

Halve it and use $sin 4 5^{\circ}$ .

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.

$sin θ = 1 \Rightarrow θ = 9 0^{\circ}$ , so $\frac{θ}{2} = 4 5^{\circ}$ .
$\frac{1}{2} sin 4 5^{\circ} = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{2 2}$ . Option (A).
1 mark

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

Where the marks are

Finds $θ = 9 0^{\circ}$ and evaluates to $\frac{1}{2 2}$ (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 paper2024 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 10

Hints

Step-by-step solution

Revise the chapter

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