# Bentuk Perkalian

### Bentuk Perkalian

###### Bentuk Perkalian

$$2 \sin A \:.\: \cos B = \sin (A + B) + \sin (A - B)$$

$$2 \cos A \:.\: \sin B = \sin (A + B) - \sin (A - B)$$

$$2 \cos A \:.\: \cos B = \cos (A + B) + \cos (A - B)$$

$$- 2 \sin A \:.\: \sin B = \cos (A + B) - \cos (A - B)$$

Contoh 01

\begin{equation*}
\begin{split}
& \int 6 \sin 3x \cos 2x \:dx\\\\
& 3 \int 2 \sin 3x \cos 2x \:dx\\\\
& {\color {blue} 2\sin A \cos B = \sin (A+B) + \sin (A - B) }\\\\
& 3 \int \sin (3x+2x) + \sin (3x - 2x) \:dx\\\\
& 3 \int \sin 5x + \sin x \:dx\\\\
& 3 \int \sin 5x \: \frac {d(5x)}{5} + 3 \int \sin x \:dx\\\\
& \bbox[5px, border: 2px solid magenta] {- \frac{3}{5} \cos 5x - 3 \cos x + c}
\end{split}
\end{equation*}

Contoh 02

\begin{equation*}
\begin{split}
& \int \sin x \sin 5x \:dx\\\\
& -\frac{1}{2}\int -2\sin x \sin 5x \:dx\\\\
& {\color {blue} -2 \sin A \sin B = \cos (A+B) - \cos (A - B) }\\\\
& -\frac{1}{2}\int \cos (x+5x) - \cos (x - 5x) \:dx\\\\
& -\frac{1}{2}\int \cos 6x - \cos (-4x) \:dx\\\\
& -\frac{1}{2}\int \cos 6x - \cos 4x \:dx\\\\
& -\frac{1}{2}\int \cos 6x \: \frac {d(6x)}{6} + \frac 12 \cos 4x \: \frac{d(4x)}{4}\\\\
& \bbox[5px, border: 2px solid magenta] {-\frac{1}{12} \sin 6x + \frac{1}{8}\sin 4x + c}
\end{split}
\end{equation*}