If 2(A+B) = √(3) and (A-B) = 1, then find the measures of angles A and B. 0°≤ A, B, (A+B) ≤ 90°.

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 23(b)

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section B, question 23(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(b) · 2 marks · Very short answerIntroduction to Trigonometry

If $2 sin (A + B) = 3$ and $cos (A - B) = 1$ , then find the measures of angles $A$ and $B$ . $0^{\circ} \leq A, B, (A + B) \leq 9 0^{\circ}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

Divide the first equation by 2 and recognise the standard angle.

Hint 2

Which angle has cosine equal to 1? Then solve the two linear equations in A and B.

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.

$sin (A + B) = \frac{3}{2} = sin 6 0^{\circ} \Rightarrow A + B = 6 0^{\circ}$ …(1)
½ mark
$cos (A - B) = 1 = cos 0^{\circ} \Rightarrow A - B = 0^{\circ}$ …(2)
½ mark
Adding (1) and (2): $2 A = 6 0^{\circ} \Rightarrow A = 3 0^{\circ}$ ; then $B = 6 0^{\circ} - 3 0^{\circ} = 3 0^{\circ}$ .
1 mark

Answer: $A = 3 0^{\circ}$ , $B = 3 0^{\circ}$

Where the marks are

$A + B = 6 0^{\circ}$ (½ mark)
$A - B = 0^{\circ}$ (½ mark)
Solves to get $A = B = 3 0^{\circ}$ (1 mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)

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 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 23(b)

Hints

Step-by-step solution

Revise the chapter

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