'Prove your courage' is correct and usable in written English.
You can use this phrase when trying to encourage someone to demonstrate or show off their courage. For example, "Don't be scared - prove your courage and take the plunge!".
They have to prove their courage and win the approval of white men.
In ancient times Hawaiian chiefs would prove their courage by diving over the cliff at Wailua Falls, 5 miles (8 km) north.
By tradition, a new regiment of young warriors is asked to confront a bull to prove its courage, inheriting the beast's strength as it expires.
This was a generation who had missed the great test of the first world war and was longing for a chance to prove its courage.
But while observers will continue to doubt his place among Britain's fistic greats, let Tuesday's shock announcement prove his courage beyond dispute.
Fate affords him the opportunity to prove his courage when he engages in a fanatical one-man chase to recover the train after it is stolen by Union spies.
So Hamilton, at 49, decided to expose himself to Burr's fire to prove his courage, but to throw away his own shot to express his aversion to dueling.
At both points, Vanya must climb a tower to prove his courage, and the consequences in both cases suggest how far he has come in his journey to adulthood.
After they prove their courage by retrieving the Rat's Tail from the Castle of Ordeal, the King of the Dragons, Bahamut, promotes each Light Warrior.
Suicide was painted as a way to escape the evils of the outside world, and Jones would force the residents into rehearsals for a revolutionary mass suicide, intended to prove their courage and faith to the crumbling and evil outside world.
The European and Asian rites were to prove courage and devotion; to say this bond is serious; we are kindred spirits in a conspiracy.
