Answer 1

\[ \cos47^\circ\cos13^\circ - \sin47^\circ \sin13^\circ\]
\[ = \cos\left( 47^\circ + 13^\circ \right) \left[\text{ Using }\cos A \cos B - \sin A \sin B = \cos\left( A + B \right) \right]\]
\[ = cos 60^\circ = \frac{1}{2}\]