Why does f[x]=Sin[2x]+Sin[3x] Not Equal a Trig Function?

[skyriver]

for example
if f[x]=Sin[2x]+Sin[3x] then f[x] can not be a Trigonometric function,
why? how many ways to prove this?

 

[HallsofIvy]

You used the word "harmonic" in your title and "trigonometric" in the text. Would you give the definition of those words that you are using?

 

[skyriver]

What i mean by a simple harmonic wave is a function which has this form f(t)=ASin[ωt+φ], where A is the amplitude, ω is the frequency, and φ is the phase,t is time.

my question is :if two two harmonic waves A1*Sin(ω1*t+φ1) and B1*Sin(ω2*t+φ2) have different frequencys ,i.e ω1 is not equal to ω2, then the sum of these two functions can not be any harmonic wave ,i.e the sum can not be function like ASin(ωt+φ) .