Question

Solve: $\sin (-{330}^o)\cdot \cos (-{300}^o)+\sin (-{420}^o)\cdot \cos {390}^o=-\frac{1}{2}$

Answer 1

$\sin (-{330}^{\circ })\cos (-{300}^{\circ })+\sin (-{420}^{\circ })\cos \left({390}^{\circ }\right)=-1/2$

$LHS=+\sin {30}^{\circ }\cos {60}^{\circ }-\sin \left({60}^{\circ }\right)\cos {30}^{\circ }$

$=\sin (30-60)=-\sin {30}^{\circ }$

$=-1/2$

$=RHS$

$LHS=RHS$