If A = y, then express A and A in terms of y.

A = √(1-y²), A = (y)/(√(1-y²))

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 23(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section B, question 23(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(b) · 2 marks · Very short answerIntroduction to Trigonometry

If $sin A = y$ , then express $cos A$ and $tan A$ in terms of $y$ .

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 identity links $sin A$ and $cos A$ ?

Hint 2

Once you have $cos A$ , use $tan A = \frac{s i n A}{c o s A}$ .

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.

Since $sin^{2} A + cos^{2} A = 1$ : $cos A = 1 - sin^{2} A = 1 - y^{2}$
1 mark
$tan A = \frac{s i n A}{c o s A} = \frac{y}{1 - y ^{2}}$
1 mark

Answer: $cos A = 1 - y^{2}$ , $tan A = \frac{y}{1 - y ^{2}}$

Where the marks are

Obtains $cos A = 1 - y^{2}$ using the identity (1 mark)
Obtains $tan A = \frac{y}{1 - y ^{2}}$ (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 paper2025 board paper, set 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 23(b)

Hints

Step-by-step solution

Revise the chapter

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