Question
Evaluate $: \sin 42^\circ \sin 48^\circ - \cos 42^\circ \cos 48^\circ $
✓
Answer
$\sin 42^\circ \sin 48^\circ - \cos 42^\circ \cos 48^\circ $
$= \sin(90^\circ - 48^\circ )\sin 48^\circ - \cos(90^\circ - 48^\circ )\cos 48^\circ $
$= \cos 48^\circ \sin 48^\circ - \sin 48^\circ \cos 48^\circ $
$= \cos 48^\circ \sin 48^\circ - \cos 48^\circ \sin 48^\circ $
$= 0$
$= \sin(90^\circ - 48^\circ )\sin 48^\circ - \cos(90^\circ - 48^\circ )\cos 48^\circ $
$= \cos 48^\circ \sin 48^\circ - \sin 48^\circ \cos 48^\circ $
$= \cos 48^\circ \sin 48^\circ - \cos 48^\circ \sin 48^\circ $
$= 0$
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