Question

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

Answer 1

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