Calculators giving wrong answer for sin75

well if you calculate sin75 with a pencil and paper: sin75= sin(45+30) = (sin45 * cos 30) - (sin30 * cos45) which equals 0.2589.
but if you plugged the numbers directly into the calculator: sin 75 you'll get 0.9659 which is a huge difference.
i really need an explanation for this dilemma.
thanks in advance.

sin75= sin(45+30) = (sin45 * cos 30) + (sin30 * cos45) = [sqrt(2)/2][sqrt(3)/2 + 1/2] = 0.9659