Question

Simplify $\cos {38}^{\circ }\cos {52}^{\circ }-\sin {38}^{\circ }\sin {52}^{\circ }$

Answer 1

$\cos 38°\cos 52°-\sin 38°\sin 52°$

$=\cos (38°+52°)$ $[\because \cos A\cos B-\sin A\sin B=\cos (A+B)]$

$=\cos 90°$

$=0$

Hence, the answer is $0.$