If x ((2 30°)/(1+² 30°) ) = y ((2 30°)/(1-² 30°) ), then x : y = (A) 1 : 1 (B) 1 : 2 (C) 2 : 1 (D) 4 : 1

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 12

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section A, question 12, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q12 · 1 mark · MCQIntroduction to Trigonometry

If $x (\frac{2 t a n 3 0 ^{\circ}}{1 + t a n ^{2} 3 0 ^{\circ}}) = y (\frac{2 t a n 3 0 ^{\circ}}{1 - t a n ^{2} 3 0 ^{\circ}})$ , then $x : y =$

(A)1 : 1
(B)1 : 2
(C)2 : 1
(D)4 : 1

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Substitute $tan 3 0^{\circ} = 1/ 3$ .

Hint 2

Simplify each bracket, then compare.

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.

$tan 3 0^{\circ} = \frac{1}{3}$ , $tan^{2} 3 0^{\circ} = \frac{1}{3}$ . LHS bracket $= \frac{2/ 3}{4/3} = \frac{3}{2}$ ; RHS bracket $= \frac{2/ 3}{2/3} = 3$ .
½ mark
$x \cdot \frac{3}{2} = y 3 \Rightarrow x = 2 y$ , so $x : y = 2 : 1$ . Option (C).
½ mark

Answer: 2 : 1, option (C)

Where the marks are

Evaluates both brackets (½ mark)
Gets x : y = 2 : 1 (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 30/6/1 (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 2025: question 12

Hints

Step-by-step solution

Revise the chapter

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