Mathematics

Problem

For a real variable

x

, consider the triple–angle expression

\cos 3x

. a. (i) Rewrite

\cos 3x

\cos(2x+x)

and expand step by step until the expression contains only powers of

\cos x

. b. (ii) Rearrange your result to obtain

\cos 3x = 4\cos^{3}x - 3\cos x

. c. (iii) Using the relation found in part (ii), determine the exact value of

\cos(90^{\circ})

by putting

x=30^{\circ}

. Verify that your result matches the well-known value.