Extremely common. Britain took and held half of whats now India, Pakistan and Bangladesh, plus Egypt, Sudan, Iraq, and etc and etc using Muslim troops, fighting other Muslims.
And for that matter so did France, for its part, in its empire.
But in those days there was not the great animosity between Christians and muzzies. There were no jihadist wars as there are now. There was no Taliban and ISIS. The Jewish state was not even created(which is the major cause of the friction between Christian and Muslim.