Mathematics

Problem

Without using trigonometric tables, answer the following: a. (i) Show that

\tan 75^\circ=2+\sqrt3

. b. (ii) Hence determine the exact values of

\sin 75^\circ

and

\cos 75^\circ

. c. (iii) Using your results from (ii), evaluate exactly

E=\sin 75^\circ\cos 15^\circ+\cos 75^\circ\sin 15^\circ