Question

Assertion (A): The value of \((\sin \theta+\cos \theta)\) is always greater than 1.

Reason (R): For \(0^{\circ} \leq \theta \leq 90^{\circ}\), the value of \(\sin \theta\) varies from 0 to 1 and the value of \(\cos \theta\) varies from 1 to 0.

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

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

Explanation:

Step 1 – Assertion: A is false. At \(\theta=0^{\circ}\), \(\sin\theta+\cos\theta=0+1=1\), so the sum is not always greater than 1.

Step 2 – Reason: R is true. Over the stated interval, sine increases from 0 to 1 while cosine decreases from 1 to 0.