Question

The value of $\cos {30}^{\circ }\cos {60}^{\circ }-\sin {30}^{\circ }\sin {60}^{\circ }$ is equal to

Answer 1

$\begin{array}{cc}\cos {30}^{\circ }\cos {60}^{\circ }-\sin {30}^{\circ }\sin {60}^{\circ }& =\frac{\sqrt{3}}{2}\times \frac{1}{2}-\frac{1}{2}\times \frac{\sqrt{3}}{2}\\ & =\frac{\sqrt{3}}{4}-\frac{\sqrt{3}}{4}\\ & =0\end{array}$

Hence proved, given expression is equal to $0.$