'to show determination' is correct and usable in written English.
You can use it when discussing someone's attitude towards something. For example, "His willingness to continue studying despite the difficulties he faced showed determination."
Some of those troops could usefully be Muslims (eg, Turks) but many should be western, to show determination and commitment.
To show determination in the battle against H.I.V. and AIDS, the leaders will be asked to halt and reverse the spread of the disease by 2015.
And so no less than those who worship ancestors in China today, Confucius had good reason to be in awe of his own ancestors and to show determination to preserve their rituals and knowledge.
The ECB president said Europe needed to show determination, confidence and a willingness to cooperate, "because the size of the challenge could actually undermine the confidence and make fear prevail over any other consideration.
The American plan was based on a simple formula: the Palestinians needed to show determination in word and deed to crack down on terror, and the Israelis had to refrain from further unilateral actions like the construction at Har Homa.
While some Republican activists and conservative lawmakers have suggested that a government shutdown might not be such a bad outcome for Republicans eager to show determination on spending cuts, the two Republican leaders — Speaker John A. Boehner of Ohio and Senator Mitch McConnell of Kentucky — have played down such talk.
How might he show determination to take all sections of the party with him, especially – given his shadow cabinet selections – its women?
Surviving a bad vacation as a family requires everyone to step up and show determination, loyalty, and yes, even courage.
She seemed to work best under pressure, and she began to show firmer determination.
The habit seems to show a determination not to be misunderstood.
Italy's prime minister wanted to show his determination to tackle the region's rubbish mountain.
