If A and B are acute angles such that (A - B) = 0 and 2(A + B) - 1 = 0, then find angles A and B.

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 25(B)

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section B, question 25(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(B) · 2 marks · Very short answerIntroduction to Trigonometry

If A and B are acute angles such that $sin (A - B) = 0$ and $2 cos (A + B) - 1 = 0$ , then find angles A and B.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

For which angle is the sine equal to 0? For which acute angle is the cosine equal to $\frac{1}{2}$ ?

Hint 2

You will get two linear equations in A and B. Add them.

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.

$sin (A - B) = 0 = sin 0^{\circ}$ , so $A - B = 0^{\circ}$ ...(1)
½ mark
$2 cos (A + B) - 1 = 0$ gives $cos (A + B) = \frac{1}{2} = cos 6 0^{\circ}$ , so $A + B = 6 0^{\circ}$ ...(2)
½ mark
Adding (1) and (2): $2 A = 6 0^{\circ}$ , so $A = 3 0^{\circ}$ .
Then from (1), $B = 3 0^{\circ}$ .
1 mark

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

Where the marks are

Gets $A - B = 0^{\circ}$ (½ mark)
Gets $A + B = 6 0^{\circ}$ (½ mark)
Solves to $A = 3 0^{\circ}$ , $B = 3 0^{\circ}$ (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 paper2023 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 25(B)

Hints

Step-by-step solution

Revise the chapter

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