1) cos^2 15 - cos^2 105 =...

Trigonometry.

cos² x = 1/2 (1 + cos 2x)
cos (180° + θ) = -cos θ

cos² 15° - cos² 105°
= 1/2 (1 + cos 30°) - 1/2 (1 + cos 210°)
= 1/2 (cos 30° - cos 210°)
= 1/2 (cos 30° + cos 30°)
= 1/2 (2)(1/2 √3)
= √3 / 2