Assertion (A): For an acute angle θ, θ is always less than 1. Reason (R): In a right-angled triangle, hypotenuse is the longest side and θ = BaseHypotenuse. (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 · Basic · Board exam 2026, set 430/5/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2026: question 19

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedIntroduction to Trigonometry

Assertion (A): For an acute angle $θ$ , $cos θ$ is always less than 1.
Reason (R): In a right-angled triangle, hypotenuse is the longest side and $cos θ = \frac{Base}{Hypotenuse}$ .

(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 430/5/1.

Hints

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

Hint 1

Compare the base with the hypotenuse.

Hint 2

Does R directly give the reason for 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.

R is true: the hypotenuse is the longest side and $cos θ =$ base/hypotenuse.
Since base < hypotenuse for an acute angle, $cos θ < 1$ ; so A is true and R explains it.
1 mark

Answer: Option (A)

Where the marks are

Both true and R correctly explains A (1 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 paper2026 board paper, set 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 19

Hints

Step-by-step solution

Revise the chapter

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