Final answer:
True, The British colonists did initially have key victories in the French and Indian War and most Indian tribes supported the British, fearing American expansion. After the war, British efforts to recoup costs led to strained relationships with the colonies despite a shared sense of identity forged during wartime.
Step-by-step explanation:
The statement 'The efforts of the British colonists were, at first, a rousing success as they experienced key victories against their rivals and their American Indian allies.' is true. During the French and Indian War, the British colonists and their mother country achieved significant military successes. Moreover, most Indian tribes and nations supported the British, which is true, as they feared American expansion would lead to a greater loss of their lands.
Post-war, however, tensions arose as the British government sought to offset war costs by tightening control over the colonies, contrary to the colonists' expectations of liberty to expand westward. An increased sense of common identity among the colonists as a result of military collaboration during the war is also true, setting the stage for the shifts in the relationship between the colonies and Great Britain that eventually led to the American Revolution.