Mathematics

Problem

To obtain an exact value for

\sin 75^{\circ}

using only the standard angles

30^{\circ}

45^{\circ}

and

60^{\circ}

, which of the following angle decompositions of

75^{\circ}

is the most direct? a)

75^{\circ}=90^{\circ}-15^{\circ}

75^{\circ}=60^{\circ}+15^{\circ}

75^{\circ}=45^{\circ}+30^{\circ}

75^{\circ}=120^{\circ}-45^{\circ}