Without using a calculator

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

Problem

Without using a calculator, evaluate two exact numerical values related to squared trigonometric functions. (i) Express

\sin^{2}15^{\circ}

entirely in terms of

\cos 30^{\circ}

. (ii) Hence find the exact value of

\sin^{2}15^{\circ}

. (iii) Using the result of part (ii), determine the exact value of

\cos^{2}75^{\circ}