Without carrying out any arithmetic calculation

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Without carrying out any arithmetic calculation, decide whether the value of

\cos 50^{\circ}\cos 25^{\circ}+\sin 50^{\circ}\sin 25^{\circ}

is greater than, equal to, or less than

\cos 25^{\circ}

. Give a brief reason.