Find the value of x if 2 cosec² 30°+ x ² 60°- 3/4² 30°= 10

MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 24(b)

From the official CBSE sample question paper for 2023-24, section B, question 24(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(b) · 2 marks · Very short answerIntroduction to Trigonometry

Find the value of x if $2 cosec^{2} 3 0^{\circ} + x sin^{2} 6 0^{\circ} - \frac{3}{4} tan^{2} 3 0^{\circ} = 10$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Recall the trigonometric ratios of 30° and 60° from the standard table.

Hint 2

cosec 30° = 2, sin 60° = √3/2 and tan 30° = 1/√3. Square each value before you substitute it.

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: $cosec 3 0^{\circ} = 2$ , $sin 6 0^{\circ} = \frac{3}{2}$ , $tan 3 0^{\circ} = \frac{1}{3}$ . Substituting them:
$2 (2)^{2} + x (\frac{3}{2})^{2} - \frac{3}{4} (\frac{1}{3})^{2} = 10$
1 mark
Simplify each term: $2 (4) + x \cdot \frac{3}{4} - \frac{3}{4} \cdot \frac{1}{3} = 10$ , that is,
$8 + \frac{3 x}{4} - \frac{1}{4} = 10$
½ mark
Multiply both sides by 4: $32 + 3 x - 1 = 40$ . So $3 x = 9$ , which gives $x = 3$ .
½ mark

Answer: $x = 3$

Where the marks are

Substitutes the correct values of cosec 30°, sin 60° and tan 30° (1 mark)
Simplifies to $8 + \frac{3 x}{4} - \frac{1}{4} = 10$ (1/2 mark)
Obtains $x = 3$ (1/2 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 paperSample paper 2023-24 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2023-24: question 24(b)

Hints

Step-by-step solution

Revise the chapter

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