Question

Find the value of the following:
$\cos {60}^o\cos {30}^o-\sin {60}^o\sin {30}^o$

Answer 1

We know that the values of the trignometric functions $\sin {60}^0=\frac{\sqrt{3}}{2}$, $\cos {30}^0=\frac{\sqrt{3}}{2}$, $\sin {30}^0=\frac{1}{2}$ and $\cos {60}^0=\frac{1}{2}$, therefore, the value of $\cos {60}^0\cos {30}^0-\sin {60}^0\sin {30}^0$ is:

$\cos {60}^0\cos {30}^0-\sin {60}^0\sin {30}^0=(\frac{\sqrt{3}}{2}\times \frac{1}{2})-(\frac{\sqrt{3}}{2}\times \frac{1}{2})=\frac{\sqrt{3}}{4}-\frac{\sqrt{3}}{4}=0$

Hence, $\cos {60}^0\cos {30}^0-\sin {60}^0\sin {30}^0=0$.