If α = (1)/(√(2)) and β = √(3), then find the value of cosec α + cosec β.

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 23(b)

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section B, question 23(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

If $sin α = \frac{1}{2}$ and $cot β = 3$ , then find the value of $cosec α + cosec β$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

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

Hint 1

Cosec is the reciprocal of sin.

Hint 2

For $β$ , use $cosec^{2} β = 1 + cot^{2} β$ . You could also recognise which standard angle has $cot = 3$ .

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.

Since $cosec α = \frac{1}{sin α}$ , we get $cosec α = \frac{1}{1/ 2} = 2$ .
½ mark
Use the identity $cosec^{2} β = 1 + cot^{2} β$ . Then $cosec β = 1 + (3)^{2} = 4 = 2$ .
1 mark
Therefore $cosec α + cosec β = 2 + 2$ , which can also be written as $2 (1 + 2)$ .
½ mark

Answer: $2 + 2$

Where the marks are

Finds $cosec α = 2$ (½ mark)
Finds $cosec β = 2$ using $1 + cot^{2} β$ or $β = 3 0^{\circ}$ (1 mark)
States the sum $2 + 2$ (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Proving Simple Trigonometric Identities

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 paper2023 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 2023: question 23(b)

Hints

Step-by-step solution

Revise the chapter

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