Question

Assertion (A): \(\tan 48^{\circ}=\cot 52^{\circ}\).

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

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. Using the stated identity, \(\tan 48^{\circ}=\cot(90^{\circ}-48^{\circ})=\cot 42^{\circ}\), which is not \(\cot 52^{\circ}\).

Step 2 – Reason: R is true; tangent of an angle equals cotangent of its complement.