$\cos(105°)$ using sum and difference identities I was trying to solve $\cos(105°)$ using sum and difference identities.
My solution:
$\cos(105°) = \cos(60°+45°)$
$\cos(60°)\cos(45°) - \sin(60°)\sin(45°)$
so,
$\frac{1}{2} \cdot \frac{\sqrt{2}}{2}$ - $\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{2}}{2}$
then,
$\frac{\sqrt{2}}{4} - \frac{\sqrt{6}}{4}$
last,
$\frac{\sqrt{2}-\sqrt{6}}{4}$
but when I try to use calculator it says,
$\frac{-\sqrt{6}+\sqrt{2}}{4}$
What part of the solution I am doing it wrong?

$a - b = a + (-b) = (-b) + a = -b + a$.
Thus,
$$\frac{\sqrt{2} - \sqrt{6}}{4} = \frac{-\sqrt{6} + \sqrt{2}}{4}$$
and both your answers are correct (they are equivalent).
