Answer:
Proved
Step-by-step explanation:
[tex]\cos{(x)} \cos{(y)} [\tan{(x)}+\tan{(y)}]\\=\cos{(x)}\cos{(y)}\times[\frac{\sin{(x)}}{\cos{(x)}}+\frac{\sin{(y)}}{\cos{(y)}}]\\\\\\\\=\cos{(x)}\cos{(y)}\times\frac{\sin{(x)}}{\cos{(x)}}+\cos{(x)}\cos{(y)}\times\frac{\sin{(y)}}{\cos{(y)}}\\\\\\\\=\cos{(y)}\times\sin{(x)}+\cos{(x)}\sin{(y)}\\\\=\sin{(x+y)}[/tex]
