Evaluate : A B + A B; if A = 30° and B = 45°.

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

CBSE Class 10 Mathematics Basic 2024: question 24

Set in the CBSE Class 10 board exam of 2024, paper 430/1/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerIntroduction to Trigonometry

Evaluate : $sin A cos B + cos A sin B$ ; if $A = 3 0^{\circ}$ and $B = 4 5^{\circ}$ .

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

Hints

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

Hint 1

Recall the standard values: $sin 3 0^{\circ} = \frac{1}{2}$ , $cos 3 0^{\circ} = \frac{3}{2}$ .

Hint 2

Both $sin 4 5^{\circ}$ and $cos 4 5^{\circ}$ equal $\frac{1}{2}$ ; substitute and add the fractions.

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.

$sin 3 0^{\circ} cos 4 5^{\circ} + cos 3 0^{\circ} sin 4 5^{\circ} = \frac{1}{2} \times \frac{1}{2} + \frac{3}{2} \times \frac{1}{2}$
1½ marks
$= \frac{1 + 3}{2 2}$ $(= \frac{6 + 2}{4})$
½ mark

Answer: $\frac{3 + 1}{2 2}$

Where the marks are

Substitutes correct values of $sin 3 0^{\circ}, cos 4 5^{\circ}, cos 3 0^{\circ}, sin 4 5^{\circ}$ (1½ marks)
Simplifies to $\frac{3 + 1}{2 2}$ (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 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 24

Hints

Step-by-step solution

Revise the chapter

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