Half angle identity

[Joe Horn]

If you mean that the correct answer is \(\cfrac{-\sqrt{2-\sqrt{3}}}{2}\), you're right, but so is Prime's answer. They're equivalent ways of expressing the same number, approximately -0.258819045103... If you didn't mean the above expression, compare with the output from https://www.wolframalpha.com/input?i=cos%28105%C2%B0%29