Are two signals that make up a periodic signal necessarily periodic?

[ChickenChakuro]

Homework Statement

If a(t) is periodic and is composition of two signals such that a(t) = b(t) + c(t), then are b(t) and c(t) necessarily periodic?

2. The attempt at a solution

I think that b(t) and c(t) must be! Is this correct?

 

[Dick]

No. b(t)=sin(t)+t. c(t)=sin(t)-t. Wasn't that easy?

 

[ChickenChakuro]

No. b(t)=sin(t)+t. c(t)=sin(t)-t. Wasn't that easy?

Indeed it was. Thanks for your help!