Assertion (A): If A + ² A = 1, then ² A + ^4 A = 1 Reason (R): ² A + ² A = 1 (A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (B) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (C) Assertion (A) is true but reason (R) is false. (D) Assertion (A) is false but reason (R) is true.

MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 20

From the official CBSE sample question paper for 2025-26, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedIntroduction to Trigonometry

Assertion (A): If $cos A + cos^{2} A = 1$ , then $sin^{2} A + sin^{4} A = 1$
Reason (R): $sin^{2} A + cos^{2} A = 1$

(A)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
(B)Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
(C)Assertion (A) is true but reason (R) is false.
(D)Assertion (A) is false but reason (R) is true.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Rearrange the given equation to isolate cos A.

Hint 2

Replace $1 - cos^{2} A$ with $sin^{2} A$ .

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 $cos A + cos^{2} A = 1$ we get $cos A = 1 - cos^{2} A = sin^{2} A$ , using (R).
Then $sin^{2} A + sin^{4} A = cos A + (cos A)^{2} = 1$ . So (A) is true, (R) is true, and (R) is the identity used to prove it. The answer is option (A).
1 mark

Answer: Option (A)

Where the marks are

Shows $cos A = sin^{2} A$ using (R) and substitutes to prove (A), option (A) (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 paperSample paper 2025-26 (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 sample paper 2025-26: question 20

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry