If A = √(3); where A is an acute angle, then find the value of (² A)/(1 + ² A).

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 23

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerIntroduction to Trigonometry

If $tan A = 3$ ; where A is an acute angle, then find the value of $\frac{s i n ^{2} A}{1 + c o s ^{2} A}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

Which standard acute angle has tangent $3$ ?

Hint 2

Substitute $sin 6 0^{\circ} = \frac{3}{2}$ and $cos 6 0^{\circ} = \frac{1}{2}$ .

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.

$tan A = 3 = tan 6 0^{\circ}$ , so $A = 6 0^{\circ}$ (A is acute).
½ mark
$\frac{s i n ^{2} 6 0 ^{\circ}}{1 + c o s ^{2} 6 0 ^{\circ}} = \frac{( \frac{3}{2} ) ^{2}}{1 + ( \frac{1}{2} ) ^{2}} = \frac{\frac{3}{4}}{\frac{5}{4}}$ .
1 mark
$= \frac{3}{5}$ .
½ mark

Answer: $\frac{3}{5}$

Where the marks are

Finds $A = 6 0^{\circ}$ (½ mark)
Substitutes $sin 6 0^{\circ}$ and $cos 6 0^{\circ}$ correctly (1 mark)
Gets $\frac{3}{5}$ (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)

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 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 23

Hints

Step-by-step solution

Revise the chapter

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