Use an identity to wrote the expression as a single trigonom

Use an identity to wrote the expression as a single trigonometric function or as a single number. 2 cos^2 75 degree - 1 squareroot 3/2 -squareroot 3/2 1/2 - 1/2

Solution

2cos²75-1

this is of the form 2cos²A - 1 which is equal to cos 2A

Therefore

2cos²75-1 = cos 2(75) = cos 150=-sqrt3/2

Hence the correct option is B