Soal yang Akan Dibahas
Nilai dari $ \frac{\sin 48^\circ + \sin 12^\circ}{\cos 78^\circ + \cos 42^\circ} \, $
adalah ....
A). $\frac{1}{2} \, $ B). $ 1 \, $ C). $ \sqrt{3} \, $ D). $ \cos 18^\circ \, $ E). $ \tan 18^\circ $
A). $\frac{1}{2} \, $ B). $ 1 \, $ C). $ \sqrt{3} \, $ D). $ \cos 18^\circ \, $ E). $ \tan 18^\circ $
$\spadesuit $ Konsep Dasar Rumus Trigonometri
1). $ \sin A + \sin B = 2\sin \left( \frac{A+B}{2} \right) . \cos \left( \frac{A-B}{2} \right) $
2). $ \cos A + \cos B = 2\cos \left( \frac{A+B}{2} \right) . \cos \left( \frac{A-B}{2} \right) $
1). $ \sin A + \sin B = 2\sin \left( \frac{A+B}{2} \right) . \cos \left( \frac{A-B}{2} \right) $
2). $ \cos A + \cos B = 2\cos \left( \frac{A+B}{2} \right) . \cos \left( \frac{A-B}{2} \right) $
$\clubsuit $ Pembahasan
*). Menyelesaikan soalnya :
$\begin{align} \frac{\sin 48^\circ + \sin 12^\circ}{\cos 78^\circ + \cos 42^\circ} & = \frac{2\sin \left( \frac{48^\circ+12^\circ}{2} \right) . \cos \left( \frac{48^\circ-12^\circ}{2} \right)}{2\cos \left( \frac{78^\circ+ 42^\circ}{2} \right) . \cos \left( \frac{78^\circ- 42^\circ}{2} \right)} \\ & = \frac{\sin \left( 30^\circ \right) . \cos \left( 18^\circ \right)}{\cos \left( 60^\circ \right) . \cos \left( 18^\circ \right)} \\ & = \frac{\sin \left( 30^\circ \right) }{\cos \left( 60^\circ \right) } = \frac{\frac{1}{2}}{\frac{1}{2}} = 1 \end{align} $
Jadi, nilai $ \frac{\sin 48^\circ + \sin 12^\circ}{\cos 78^\circ + \cos 42^\circ} = 1 . \, \heartsuit $
*). Menyelesaikan soalnya :
$\begin{align} \frac{\sin 48^\circ + \sin 12^\circ}{\cos 78^\circ + \cos 42^\circ} & = \frac{2\sin \left( \frac{48^\circ+12^\circ}{2} \right) . \cos \left( \frac{48^\circ-12^\circ}{2} \right)}{2\cos \left( \frac{78^\circ+ 42^\circ}{2} \right) . \cos \left( \frac{78^\circ- 42^\circ}{2} \right)} \\ & = \frac{\sin \left( 30^\circ \right) . \cos \left( 18^\circ \right)}{\cos \left( 60^\circ \right) . \cos \left( 18^\circ \right)} \\ & = \frac{\sin \left( 30^\circ \right) }{\cos \left( 60^\circ \right) } = \frac{\frac{1}{2}}{\frac{1}{2}} = 1 \end{align} $
Jadi, nilai $ \frac{\sin 48^\circ + \sin 12^\circ}{\cos 78^\circ + \cos 42^\circ} = 1 . \, \heartsuit $
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