Evaluate : ² 30°+ ² 45°- 0°· 45°

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2024: question 21

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, 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 : $sin^{2} 3 0^{\circ} + cos^{2} 4 5^{\circ} - cos 0^{\circ} \cdot tan 4 5^{\circ}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

Recall the trigonometric ratio table for 0°, 30° and 45°.

Hint 2

$sin 3 0^{\circ} = \frac{1}{2}$ and $cos 4 5^{\circ} = \frac{1}{2}$ ; square them before adding.

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.

Substitute the standard values $sin 3 0^{\circ} = \frac{1}{2}$ , $cos 4 5^{\circ} = \frac{1}{2}$ , $cos 0^{\circ} = 1$ , $tan 4 5^{\circ} = 1$ :
$(\frac{1}{2})^{2} + (\frac{1}{2})^{2} - 1 \times 1$
1½ marks
$= \frac{1}{4} + \frac{1}{2} - 1 = \frac{1 + 2 - 4}{4} = - \frac{1}{4}$
½ mark

Answer: $- \frac{1}{4}$

Where the marks are

Substitutes correct values of $sin 3 0^{\circ}$ , $cos 4 5^{\circ}$ , $cos 0^{\circ}$ and $tan 4 5^{\circ}$ (1½ marks)
Simplifies to $- \frac{1}{4}$ (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 430/5/1 (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 21

Hints

Step-by-step solution

Revise the chapter

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