Question
Without using tables, evaluate the following$: \sin 60^\circ \sin 30^\circ + \cos 30^\circ \cos 60^\circ $
✓
Answer
$\sin 60^{\circ} \sin 30^{\circ}+\cos 30^{\circ} \cos 60^{\circ} .$
$ \sin 60^{\circ}=\frac{\sqrt{3}}{2}$
$ \sin 30^{\circ}=\frac{1}{2}$
$ \cos 30^{\circ}=\frac{\sqrt{3}}{2}$
$ \cos 60^{\circ}=\frac{1}{2}$
$ \sin 60^{\circ} \sin 30^{\circ}+\cos 30^{\circ} \cos 60^{\circ}$
$ =\frac{\sqrt{3}}{2} \times \frac{1}{2}+\frac{\sqrt{3}}{2} \times \frac{1}{2}$
$ =\frac{\sqrt{3}}{4}+\frac{\sqrt{3}}{4}$
$ =\frac{2 \sqrt{3}}{4}$
$ =\frac{\sqrt{3}}{2}$
$ \sin 60^{\circ}=\frac{\sqrt{3}}{2}$
$ \sin 30^{\circ}=\frac{1}{2}$
$ \cos 30^{\circ}=\frac{\sqrt{3}}{2}$
$ \cos 60^{\circ}=\frac{1}{2}$
$ \sin 60^{\circ} \sin 30^{\circ}+\cos 30^{\circ} \cos 60^{\circ}$
$ =\frac{\sqrt{3}}{2} \times \frac{1}{2}+\frac{\sqrt{3}}{2} \times \frac{1}{2}$
$ =\frac{\sqrt{3}}{4}+\frac{\sqrt{3}}{4}$
$ =\frac{2 \sqrt{3}}{4}$
$ =\frac{\sqrt{3}}{2}$
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