Question
Prove that$ : \cos60^\circ . \cos30^\circ - \sin60^\circ . \sin30^\circ = 0$
✓
Answer
$ \text{ L.H.S. }=\cos 60^{\circ} \cdot \cos 30^{\circ}-\sin 60^{\circ} \cdot \sin 30^{\circ}$
$ =\frac{1}{2} \times \frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2} \times \frac{1}{2}$
$ =\frac{\sqrt{3}}{4}-\frac{\sqrt{3}}{4}$
$ =0$
$ =\text{ R.H.S. }$
$ =\frac{1}{2} \times \frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2} \times \frac{1}{2}$
$ =\frac{\sqrt{3}}{4}-\frac{\sqrt{3}}{4}$
$ =0$
$ =\text{ R.H.S. }$
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