Mathematics

Problem

Find the exact value of each expression without the aid of a calculator: a. (i)

S=\sin 75^\circ\cos 30^\circ-\cos 75^\circ\sin 30^\circ

b. (ii)

P=\sin 75^\circ\cos 15^\circ-\cos 75^\circ\sin 15^\circ

c. (iii)

T=\dfrac{\tan 75^\circ-\tan 45^\circ}{1+\tan 75^\circ\tan 45^\circ}