If sin(A - B) = 1/2 and cos(A + B) = 1/2, 0° B, then find the values of A and B.

MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 24

From the official CBSE sample question paper for 2024-25, 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

If $s in (A - B) = \frac{1}{2}$ and $cos (A + B) = \frac{1}{2}$ , $0^{\circ} < A + B < 9 0^{\circ}$ and $A > B$ , then find the values of $A$ and $B$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Which standard angle has sine $\frac{1}{2}$ ? Which has cosine $\frac{1}{2}$ ?

Hint 2

You 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.

$sin (A - B) = \frac{1}{2} = sin 3 0^{\circ} \Rightarrow A - B = 3 0^{\circ}$ …(i)
½ mark
$cos (A + B) = \frac{1}{2} = cos 6 0^{\circ} \Rightarrow A + B = 6 0^{\circ}$ …(ii)
½ mark
Adding (i) and (ii): $2 A = 9 0^{\circ} \Rightarrow A = 4 5^{\circ}$
½ mark
Substituting in (ii): $B = 6 0^{\circ} - 4 5^{\circ} = 1 5^{\circ}$
½ mark

Answer: $A = 4 5^{\circ}$ , $B = 1 5^{\circ}$

Where the marks are

$A - B = 3 0^{\circ}$ (½ mark)
$A + B = 6 0^{\circ}$ (½ mark)
$A = 4 5^{\circ}$ (½ mark)
$B = 1 5^{\circ}$ (½ 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 paperSample paper 2024-25 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 24

Hints

Step-by-step solution

Revise the chapter

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