Question

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 = "Base"/"Hypotenuse"`.

Options

• Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

• Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Explanation:

In a right-angled triangle, the hypotenuse is indeed the longest side.

Since `cos θ = "Base"/"Hypotenuse"` and the base is always shorter than the hypotenuse, the value of cos θ is always less than 1.

For an acute angle (less than 90°), cos θ is positive and less than 1.

Therefore, the assertion is true and the reason correctly explains why.