If (A – B) = 1/2 and (A + B) = √(3), 0°≤ A + B B then find the values of A and B.

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 21

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerIntroduction to Trigonometry

If $sin (A - B) = \frac{1}{2}$ and $tan (A + B) = 3$ , $0^{\circ} \leq A + B < 9 0^{\circ}$ , $A > B$ then find the values of A and B.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

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

Hint 2

Write two equations, one for $A - B$ and one for $A + B$ .

Hint 3

Add the two equations to find A, then substitute to get 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.

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

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

Where the marks are

Obtains $A - B = 3 0^{\circ}$ (½ mark)
Obtains $A + B = 6 0^{\circ}$ (½ mark)
Solves to get $A = 4 5^{\circ}$ , $B = 1 5^{\circ}$ (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 paper2026 board paper, set 430/4/1 (Basic): 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 Basic 2026: question 21

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry