+584 sin(x+y)=sinx*cosy+cosx*siny
sin(x-y)=sinx*cosy-cosx*siny
so, sin(x+y)+sin(x-y)=sinx*cosy+cosx*siny+sinx*cosy-cosx*siny=2sinx*cosy
sinx*cosy=1/2[sin(x+y)+sin(x-y)]
orginal qustion=6*sin(47y)*cos(21y)=（1/2）*6*[sin(47y+21y)+sin(47y-21y)=3*[sin68y+sin26y]
=3sin68y+3sin26y
+26393 Write the product as a sum: 6sin(47y)cos(21y) = ?
$$\boxed{
\small{\text{
Formula:
$
\begin{array}{rcl}
\sin u+\sin v=2\sin \frac{u+v}{2}\cos \frac{u-v}{2}
\end{array}
$}}
}$$
$$\small{\text{$
\begin{array}{rcl}
47y = \dfrac{u+v}{2} \qquad 21y=\dfrac{u-v}{2}\\\\
u=\dfrac{u+v}{2}+\dfrac{u-v}{2}=47y+21y=68y\\\\
v=\dfrac{u+v}{2}-\dfrac{u-v}{2}=47y-21y=26y\\\\
\end{array}
$}}$$
$$\small{\text{$
\begin{array}{rcl}
\sin u+\sin v&=&2\sin \frac{u+v}{2}\cos \frac{u-v}{2}\\\\
\sin {(68y)}+\sin {(26y)} &=&2\sin{( 47y )}\cos{( 21y )} \quad | \quad \cdot 3 \\\\
3\sin {(68y)}+3\sin {(26y)} &=&6\sin{( 47y )}\cos{( 21y )}
\end{array}
$}}$$
