In a triangle ABC, sec A (sin B cos C + cos B sin C) equals:

Correct option is B

​$$\text{Given:} \quad \sec A \left( \sin B \cos C + \cos B \sin C \right)\text{Using the identity:} \quad \sin B \cos C + \cos B \sin C = \sin \left( B + C \right)\\\text{In triangle ABC:} \quad B + C = \pi - A \\\Rightarrow \sin \left( B + C \right) = \sin \left( \pi - A \right) = \sin A\\\text{Substitute into the original expression:}\quad \sec A \cdot \sin A = \frac{1}{\cos A} \cdot \sin A = \tan A$$​​