Question

Assertion (A): The value of \((\cos ^{2} 24^{\circ}-\sin ^{2} 66^{\circ})\) is positive.

Reason (R): \(0^{\circ} \leq \theta \leq 90^{\circ} \Rightarrow \cos \left(90^{\circ}-\theta\right)=\sin \theta\).

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

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

Explanation:

Step 1 – Assertion: A is false. Since \(24^{\circ}=90^{\circ}-66^{\circ}\), the stated identity gives \(\cos 24^{\circ}=\sin 66^{\circ}\). Hence, \(\cos^{2}24^{\circ}-\sin^{2}66^{\circ}=0\), which is not positive.

Step 2 – Reason: R is true; it is the complementary-angle identity.