Mathematics

Problem

Let

A=105^{\circ}

. Work through the steps below. a. (i) Write

A

as a suitable sum or difference of two standard angles and hence find the exact values of

\sin 105^{\circ}

and

\cos 105^{\circ}

. b. (ii) Show that

\sin 105^{\circ}=\cos 15^{\circ}

. c. (iii) Using the results from parts (i) and (ii), evaluate

\sin 105^{\circ}+\sin 15^{\circ}

in simplest radical form.