Answer the following questions about .

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Answer the following questions about

\cos3\theta

. (i) Express

\cos3\theta

entirely in terms of

\cos\theta

without involving

\sin\theta

. (ii) Show that the expression obtained in part (i) can be written as

\cos3\theta = 4\cos^{3}\theta - 3\cos\theta

. (iii) Taking

\theta = 20^{\circ}

, use the result of part (ii) to evaluate

\cos60^{\circ}

and verify that it equals

\dfrac{1}{2}