Question

Evaluate each of the following in the simplest form :
$cos{60}^{\circ }cos{30}^{\circ }-sin{60}^{\circ }sin{30}^{\circ }$

Answer 1

We have,
$cos{60}^{\circ }cos{30}^{\circ }-sin{60}^{\circ }sin{30}^{\circ }=\frac{1}{2}\times \frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2}\times \frac{1}{2}=\frac{\sqrt{3}}{4}-\frac{\sqrt{3}}{4}=0$