Maths · Trigonometry · chapter 8 of 14

Class 10 Maths Chapter 8: Introduction to Trigonometry Assertion-reason questions with answers

2 assertion-reason questions on Introduction to Trigonometry, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): There is no acute angle A for which 7 sin A = 8. Reason (R): In a right triangle the hypotenuse is the longest side.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

7 sin A = 8 means sin A = 8/7. sin A = opposite ÷ hypotenuse, and the hypotenuse is longer than the opposite side, so sin A < 1 for an acute angle; 8/7 > 1 is impossible. R is the reason A holds.

Question 2
Assertion (A): tan 45° = 1. Reason (R): sin²A + cos²A = 1 for 0° ≤ A ≤ 90°.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Both are true: tan 45° = 1 because the legs of a 45° right triangle are equal, and the identity is true. The identity does not explain the value of tan 45°.

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