Evaluate: 5 cosec² 45°- 3² 90°+ 5 0°.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 21

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerIntroduction to Trigonometry

Evaluate: $5 cosec^{2} 4 5^{\circ} - 3 sin^{2} 9 0^{\circ} + 5 cos 0^{\circ}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

Recall the trigonometric table values for 0°, 45° and 90°.

Hint 2

cosec 45° is the reciprocal of sin 45° = 1/√2; square it before multiplying by 5.

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.

Use the standard values: $cosec 4 5^{\circ} = 2$ , $sin 9 0^{\circ} = 1$ , $cos 0^{\circ} = 1$ . Substituting: $5 (2)^{2} - 3 (1)^{2} + 5 (1)$
1½ marks
$= 10 - 3 + 5 = 12$
½ mark

Answer: 12

Where the marks are

Substitutes correct values of cosec 45°, sin 90°, cos 0° (1½ marks)
Simplifies to 12 (½ 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 paper2023 board paper, set 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 21

Hints

Step-by-step solution

Revise the chapter

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