Assertion (A): 2θ is not defined at θ = 45°. Reason (R): 90°≠ 90°. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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 · Board exam 2026, set 30/3/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2026: question 20

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, 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): $tan 2 θ$ is not defined at $θ = 4 5^{\circ}$ . Reason (R): $sin 9 0^{\circ} \neq = cos 9 0^{\circ}$ .

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

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

Write tan 90° as sin 90°/cos 90°.

Hint 2

What makes a fraction undefined? Is that what R says?

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.

At $θ = 4 5^{\circ}$ , $tan 2 θ = tan 9 0^{\circ} = \frac{sin 9 0 ^{\circ}}{cos 9 0 ^{\circ}} = \frac{1}{0}$ , which is not defined. So (A) is true.
$sin 9 0^{\circ} = 1$ and $cos 9 0^{\circ} = 0$ , so (R) is true. However, $tan 9 0^{\circ}$ is undefined because $cos 9 0^{\circ} = 0$ , not because $sin 9 0^{\circ} \neq = cos 9 0^{\circ}$ . So (R) does not explain (A), which is option (B).
1 mark

Answer: Option (B)

Where the marks are

Chooses option (B) (1 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 paper2026 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 20

Hints

Step-by-step solution

Revise the chapter

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