Question

Without using calculator, find the value of $\cos {570}^o.\sin {510}^o+\sin (-{330}^o).\cos (-{390}^o)$.

Answer 1

$\begin{array}{c}\cos {570}^0\cdot \sin {510}^0+\sin \left(-{33}^0\right)\cdot \cos \left(-{390}^0\right)\\ degreechangeintoradius\\ \Rightarrow \cos \left(\pi +{30}^0\right)\cdot \sin \left(3\pi -{30}^0\right)-\sin \left(2\pi -{30}^0\right)\cos \left(2\pi +3\right)\\ \Rightarrow -\cos {30}^0\times \sin {30}^0+\sin {30}^0\times \cos {30}^0\\ \Rightarrow \frac{-\sqrt{3}}{2}\times \frac{1}{2}+\frac{1}{2}\times \frac{\sqrt{3}}{2}=0Ans\end{array}$