Question

Assertion (A): The value of \(\tan 1^{\circ} \cdot \tan 11^{\circ} \cdot \tan 21^{\circ} \cdot \tan 69^{\circ} \cdot \tan 79^{\circ} \cdot \tan 89^{\circ}\) is 1.

Reason (R): For \(0^{\circ}<\theta<90^{\circ}\), we have \(\tan \left(90^{\circ}-\theta\right)=\cot \theta\).

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. Pair the complementary angles: \(1^{\circ}\) with \(89^{\circ}\), \(11^{\circ}\) with \(79^{\circ}\) and \(21^{\circ}\) with \(69^{\circ}\). Each paired product is 1, so the full product is 1.

Step 2 – Reason: R is true. It states the tangent–cotangent complementary-angle identity.

Step 3 – Link: Each paired tangent product reduces to \(\tan\theta\cot\theta=1\) by R, so R correctly explains A.