Sine plus Sine/Examples/Sine 2 x plus Sine 5 x equals Sine 4 x

Examples of Use of Prosthaphaeresis Formula for Sine plus Sine
The equation
 * $\sin 3 x + \sin 5 x = \sin 4 x$

has the general solution:
 * $\set {\dfrac {n \pi} 4 : n \in \Z} \cup \set {2 n \pi \pm \dfrac \pi 3: n \in \Z}$

Proof
Hence the result.