If (A+B) = 1 and (A-B) = (√(3))/(2), 0°< A,B < 90°, find the measure of angles A and B.

MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 22

From the official CBSE sample question paper for 2025-26, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerIntroduction to Trigonometry

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

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Which angle has sine equal to 1, and which has cosine equal to $\frac{3}{2}$ ?

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.

$sin (A + B) = 1 = sin 9 0^{\circ}$ , so $A + B = 9 0^{\circ}$ . Also $cos (A - B) = \frac{3}{2} = cos 3 0^{\circ}$ , so $A - B = 3 0^{\circ}$ (taking $A > B$ ).
1 mark
Adding the two equations: $2 A = 12 0^{\circ}$ , so $A = 6 0^{\circ}$ . Then $B = 9 0^{\circ} - 6 0^{\circ} = 3 0^{\circ}$ .
1 mark

Answer: A = 60°, B = 30°

Where the marks are

Forms $A + B = 9 0^{\circ}$ and $A - B = 3 0^{\circ}$ (1 mark)
Solves to get $A = 6 0^{\circ}$ , $B = 3 0^{\circ}$ (1 mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
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 paperSample paper 2025-26 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2025-26: question 22

Hints

Step-by-step solution

Revise the chapter

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