Question

Assertion (A): The value of \((\sin 80^{\circ}-\cos 80^{\circ})\) is positive.

Reason (R): \(45^{\circ}<\theta \leq 90^{\circ} \Rightarrow \sin \theta>\cos \theta\).

Options

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

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

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

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

Explanation:

Step 1 – Assertion: A is true because \(80^{\circ}\) lies between \(45^{\circ}\) and \(90^{\circ}\), so \(\sin 80^{\circ}>\cos 80^{\circ}\). Therefore, their difference is positive.

Step 2 – Reason: R is true; for angles greater than \(45^{\circ}\) and at most \(90^{\circ}\), sine exceeds cosine.

Step 3 – Link: Applying R to \(\theta=80^{\circ}\) directly establishes A.