Answer the following questions related to the difference of two cosines.

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Answer the following questions related to the difference of two cosines. (i) Prove that

\cos x - \cos 3x = 2\sin 2x\,\sin x

for all real

x

." (ii) Using the result from part (i), evaluate

\cos 15^{\circ} - \cos 45^{\circ}