Mathematics

Problem

(a) Express each of

\sin75^{\circ}

and

\sin15^{\circ}

in terms of

\sin30^{\circ}

\cos30^{\circ}

\sin45^{\circ}

and

\cos45^{\circ}

. (b) Hence, show that

\sin75^{\circ}+\sin15^{\circ}=\dfrac{\sqrt6}{2}