If (A + B) = √(3) and (A - B) = (1)/(√(3)), 0° B, then the value of A and B respectively are: (A) 60°, 30° (B) 60°, 45° (C) 45°, 15° (D) 60°, 15°

MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 8

From the official CBSE sample question paper for 2026-27, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQIntroduction to Trigonometry

If $tan (A + B) = 3$ and $tan (A - B) = \frac{1}{3}$ , $0^{\circ} < A + B < 9 0^{\circ}$ , $A > B$ , then the value of A and B respectively are:

(A) $6 0^{\circ}, 3 0^{\circ}$
(B) $6 0^{\circ}, 4 5^{\circ}$
(C) $4 5^{\circ}, 1 5^{\circ}$
(D) $6 0^{\circ}, 1 5^{\circ}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Which angles have tangent √3 and 1/√3?

Hint 2

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.

$tan (A + B) = 3 \Rightarrow A + B = 6 0^{\circ}$ ...(i) and $tan (A - B) = \frac{1}{3} \Rightarrow A - B = 3 0^{\circ}$ ...(ii).
Add (i) and (ii): $2 A = 9 0^{\circ}$ , so $A = 4 5^{\circ}$ and $B = 1 5^{\circ}$ . This is option (C).
1 mark

Answer: A = 45°, B = 15°, option (C)

Where the marks are

Forms A + B = 60° and A − B = 30° and solves them (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 2026-27 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 8

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry