Evaluate : 4 ² 60°² 45°– 2 ² 30°² 60°

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2024: question 22

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerIntroduction to Trigonometry

Evaluate : $4 sin^{2} 6 0^{\circ} tan^{2} 4 5^{\circ} -2 sec^{2} 3 0^{\circ} tan^{2} 6 0^{\circ}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

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

Hint 1

Recall the standard values: $sin 6 0^{\circ}$ , $tan 4 5^{\circ}$ , $sec 3 0^{\circ}$ , $tan 6 0^{\circ}$ .

Hint 2

$sec 3 0^{\circ} = \frac{1}{c o s 3 0 ^{\circ}} = \frac{2}{3}$ ; square each value before multiplying.

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.

Substituting $sin 6 0^{\circ} = \frac{3}{2}$ , $tan 4 5^{\circ} = 1$ , $sec 3 0^{\circ} = \frac{2}{3}$ , $tan 6 0^{\circ} = 3$ :
$4 (\frac{3}{2})^{2} (1)^{2} - 2 (\frac{2}{3})^{2} (3)^{2} = 4 \cdot \frac{3}{4} \cdot 1 - 2 \cdot \frac{4}{3} \cdot 3$
1½ marks
$= 3 - 8 = - 5$
½ mark

Answer: $- 5$

Where the marks are

Substitutes correct values of all four trigonometric ratios (1½ marks)
Simplifies to $- 5$ (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 paper2024 board paper, set 430/3/1 (Basic): 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 Basic 2024: question 22

Hints

Step-by-step solution

Revise the chapter

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