Finding Fundamental Period of x(t) with 2 Exponentials

[EvLer]

I can't get my answer match up with correct answer in the book:
i need to find fundamental period of this signal:

x(t) = 2 cos(10t + 1) - sin(4t -1)

i used formula for cosine Acos(wt + a) = ... that gives two exponentials... so I got pi/10 instead of pi for answer...
any help is appreciated

 

[Astronuc]

x(t) = 2 cos(10t + 1) - sin(4t -1)

Is there an $\omega$ missing in this formula?

The +1 and -1 are phase shifts.

10 and 4 share a gcf of 2.

IIRC, there may be a relationship between gcf and the fundamental frequency.