Question

\[\cos A = \frac{\sqrt{3}}{2}\] and \[\sin B = \frac{1}{2}\]

Assertion (A): \[\tan(A + B) = \sqrt{3}\]

Reason (R): \[\cos A = \frac{\sqrt{3}}{2} \Rightarrow A = 30^\circ\]

\[\sin B = \frac{1}{2} \Rightarrow B = 30^\circ\]

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Given, cos A = \[\frac{\sqrt3}{2}\]​​ and sin B = \[\frac{1}{2}\]

⇒ cos A = cos 30° and sin B = sin 30°

⇒ A = 30° and B = 30°

So, reason (R) is true.

tan(A + B) = tan(30° + 30°) = tan 60° = \[\sqrt3\]

Thus, tan (A + B) = \[\sqrt3\]

So, assertion (A) is true.

∴ Both A and R are true and R is correct reason for A.