Find the values of A and B (0°≤ A < 90°, 0°≤ B < 90°), if (A + B) = 1 and (A - B) = (1)/(√(3)).

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 24(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(a) · 2 marks · Very short answerIntroduction to Trigonometry

Find the values of A and B ( $0^{\circ} \leq A < 9 0^{\circ}$ , $0^{\circ} \leq B < 9 0^{\circ}$ ), if $tan (A + B) = 1$ and $tan (A - B) = \frac{1}{3}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

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

Hint 1

Which standard angles have tangent equal to 1 and to $\frac{1}{3}$ ?

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.

$tan (A + B) = 1 = tan 4 5^{\circ} \Rightarrow A + B = 4 5^{\circ}$ ...(1)
½ mark
$tan (A - B) = \frac{1}{3} = tan 3 0^{\circ} \Rightarrow A - B = 3 0^{\circ}$ ...(2)
½ mark
Adding (1) and (2): $2 A = 7 5^{\circ} \Rightarrow A = 37. 5^{\circ}$ . Then $B = 4 5^{\circ} - 37. 5^{\circ} = 7. 5^{\circ}$ .
1 mark

Answer: A = 37.5°, B = 7.5°

Where the marks are

Writes $A + B = 4 5^{\circ}$ (½ mark)
Writes $A - B = 3 0^{\circ}$ (½ mark)
Solves to get $A = 37. 5^{\circ}$ and $B = 7. 5^{\circ}$ (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 paper2025 board paper, set 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 24(a)

Hints

Step-by-step solution

Revise the chapter

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