Sin^2 (75) - cos^2 (75) = ?

There are 2 ways of solving this:

1: puting numbers in calculator and get answer

2: try to simplify this and than calculate.

We will do second way.

there is trigonometric formula: cos2α = cos^2 (α) - sin^2 (α)

if we take "-" in front of our expression:

- (cos^2 (75) - sin^2 (75)) = - cos (2*75) = - cos (150) = - √3/2

answer is - √3/2