If 4² 45°- ² 60°+ ² 60°+ p = 3/4, then find the value of p.

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

CBSE Class 10 Mathematics Standard 2023: question 22(a)

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section B, question 22(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(a) · 2 marks · Very short answerIntroduction to Trigonometry

If $4 cot^{2} 4 5^{\circ} - sec^{2} 6 0^{\circ} + sin^{2} 6 0^{\circ} + p = \frac{3}{4}$ , then find the value of $p$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

Recall the standard values: $cot 4 5^{\circ}$ , $sec 6 0^{\circ}$ and $sin 6 0^{\circ}$ .

Hint 2

Square each value before substituting, then simplify the left side.

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 $cot 4 5^{\circ} = 1$ , $sec 6 0^{\circ} = 2$ and $sin 6 0^{\circ} = \frac{3}{2}$ :
$4 (1)^{2} - (2)^{2} + (\frac{3}{2})^{2} + p = \frac{3}{4}$
1 mark
$4 - 4 + \frac{3}{4} + p = \frac{3}{4}$
½ mark
$\Rightarrow p = 0$
½ mark

Answer: $p = 0$

Where the marks are

Substitutes the correct values of $cot 4 5^{\circ}$ , $sec 6 0^{\circ}$ and $sin 6 0^{\circ}$ (1 mark)
Simplifies to $4 - 4 + \frac{3}{4} + p = \frac{3}{4}$ (½ mark)
Gets $p = 0$ (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 paper2023 board paper, set 30/2/1 (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 22(a)

Hints

Step-by-step solution

Revise the chapter

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