If 2 A = 3, then the value of (4 A + 3 A)/(4 A - 3 A) is (A) (7)/(√(13)) (B) (1)/(√(13)) (C) 3 (D) does not exist

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 6

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section A, question 6, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q6 · 1 mark · MCQIntroduction to Trigonometry

If $2 tan A = 3$ , then the value of $\frac{4 sin A + 3 cos A}{4 sin A - 3 cos A}$ is

(A) $\frac{7}{13}$
(B) $\frac{1}{13}$
(C)3
(D)does not exist

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

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

Hint 1

Try to express the fraction in terms of $tan A$ only.

Hint 2

Divide every term of the numerator and denominator by $cos A$ .

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.

From $2 tan A = 3$ we get $tan A = \frac{3}{2}$ .
Divide the numerator and denominator by $cos A$ : $\frac{4 tan A + 3}{4 tan A - 3} = \frac{6 + 3}{6 - 3} = 3$ . Option (C).
1 mark

Answer: 3, option (C)

Where the marks are

Converts to $tan A$ and evaluates to 3, option (C) (1 mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Proving Simple Trigonometric Identities

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 paper2023 board paper, set 30/1/1 (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 2023: question 6

Hints

Step-by-step solution

Revise the chapter

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