If 4k = ² 60°- 2 cosec² 30°- 2² 30°, then find the value of k.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 21

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, 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

If $4 k = tan^{2} 6 0^{\circ} - 2 cosec^{2} 3 0^{\circ} - 2 tan^{2} 3 0^{\circ}$ , then find the value of k.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

Write down the values of $tan 6 0^{\circ}$ , $cosec 3 0^{\circ}$ and $tan 3 0^{\circ}$ first.

Hint 2

Square each value, multiply by its coefficient, then combine. Divide by 4 at the end.

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: $tan 6 0^{\circ} = 3$ , $cosec 3 0^{\circ} = 2$ , $tan 3 0^{\circ} = \frac{1}{3}$ .
$4 k = (3)^{2} - 2 (2)^{2} - 2 (\frac{1}{3})^{2} = 3 - 8 - \frac{2}{3} = - \frac{17}{3}$
1½ marks
$k = - \frac{17}{3} \div 4 = - \frac{17}{12}$
½ mark

Answer: $k = - \frac{17}{12}$

Where the marks are

Substitutes the correct trigonometric values and simplifies to $4 k = - \frac{17}{3}$ (1½ marks)
Obtains $k = - \frac{17}{12}$ (½ 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 paper2025 board paper, set 30/3/1 (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 2025: question 21

Hints

Step-by-step solution

Revise the chapter

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