g and h are bounded functions

[Lolyta]

Hello. I need help with this problem:
If g and h are real and continuous functions with g(x-y)=g(x)g(y)+h(x)h(y) for all x,y real.
How could I proff they are bounded??

I have think a lot and I found that for example g= cos and h = sin could be these fuctions (but it must to be more).

Also I have tried to replace y=0:

, x=0 :

, x=y :

, x=-y:

.

But I don't get anything.

Thanks for every suggestion.