Question : $\sin 600^\circ \cos 750^\circ+\sin 150^\circ \cos 240^\circ=?$
Option 1: $\frac{2}{3}$
Option 2: $1$
Option 3: $\frac{1}{2}$
Option 4: $-1$
Correct Answer: $-1$
Solution :
$\sin 600^\circ \cos 750^\circ+\sin 150^\circ \cos 240^\circ$
$=\sin (540^\circ+60^\circ) \cos (720^\circ+30^\circ)+\sin (180^\circ-30^\circ) \cos (180^\circ+60^\circ)$
$= -\sin 60^\circ\cos 30^\circ + \sin 30^\circ ×(-\cos 60^\circ)$
$= (-\frac{\sqrt3}{2}$ ×$\frac{\sqrt3}{2})$ + $(\frac{1}{2} × \frac{-1}{2})$
$= \frac{-3}{4} -\frac{1}{4} = –1$
Hence, the correct answer is $-1$.
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