Sine plus Sine/Examples

Examples of Use of Sine plus Sine

$\sin 40 \degrees$ plus $\sin 60 \degrees$

$\sin 40 \degrees + \sin 60 \degrees = 2 \sin 50 \degrees \cos 10 \degrees$

$\sin 2 A$ plus $\sin 6 A$

$\sin 2 A + \sin 6 A = 2 \sin 4 A \cos 2 A$

Solution to $\sin 2 x + \sin 5 x = \sin 4 x$

The equation

$\sin 3 x + \sin 5 x = \sin 4 x$

has the general solution:

$\set {\dfrac {n \pi} 4 : n \in \Z} \cup \set {2 n \pi \pm \dfrac \pi 3: n \in \Z}$