Let 2A+B and A+2B be acute angles such that (2A+B) = (√(3))/(2) and (A+2B) = 1. Find the value of (4A-7B).

A = 25°, B = 10°; (4A - 7B) = √(3)

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 30(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section C, question 30(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(b) · 3 marks · Short answerIntroduction to Trigonometry

Let $2 A + B$ and $A + 2 B$ be acute angles such that $sin (2 A + B) = \frac{3}{2}$ and $tan (A + 2 B) = 1$ . Find the value of $cot (4 A - 7 B)$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

Which acute angle has sine $\frac{3}{2}$ ? Which has tangent 1?

Hint 2

You get two linear equations in A and B; add and subtract them.

Hint 3

Substitute A and B into $4 A - 7 B$ and use the standard value of cot.

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.

$sin (2 A + B) = \frac{3}{2} = sin 6 0^{\circ} \Rightarrow 2 A + B = 6 0^{\circ}$ ...(1)
½ mark
$tan (A + 2 B) = 1 = tan 4 5^{\circ} \Rightarrow A + 2 B = 4 5^{\circ}$ ...(2)
½ mark
Adding (1) and (2): $3 A + 3 B = 10 5^{\circ} \Rightarrow A + B = 3 5^{\circ}$ . Subtracting (2) from (1): $A - B = 1 5^{\circ}$ . Hence $A = 2 5^{\circ}$ .
½ mark
$B = 1 0^{\circ}$
½ mark
$4 A - 7 B = 10 0^{\circ} - 7 0^{\circ} = 3 0^{\circ}$ , so $cot (4 A - 7 B) = cot 3 0^{\circ}$
½ mark
$= 3$
½ mark

Answer: $A = 2 5^{\circ}$ , $B = 1 0^{\circ}$ ; $cot (4 A - 7 B) = 3$

Where the marks are

Obtains $2 A + B = 6 0^{\circ}$ (½ mark)
Obtains $A + 2 B = 4 5^{\circ}$ (½ mark)
Finds $A = 2 5^{\circ}$ (½ mark) and $B = 1 0^{\circ}$ (½ mark)
Gets $4 A - 7 B = 3 0^{\circ}$ (½ mark)
Final value $3$ (½ 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 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 30(b)

Hints

Step-by-step solution

Revise the chapter

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