Question

求证：tan37.5º=√6 √3-√2-2

求证：tan37.5º=√6+√3-√2-2详细清楚点

Answer 1

sin75°=sin(45°+30°)=sin45°cos30°+cos45°sin30°=(根号6+根号2)/4
cos²75°=1-sin²75°
cos75°=(根号6-根号2)/4

tan37.5°
=tan(1/2×75°)
=(1-cos75°)/sin75°
=[1-(根号6-根号2)/4]×4/(根号6+根号2)
=[(4-根号6+根号2)(根号6-根号2)]/[(根号6+根号)(根号6-根号2)]
=(4根号6+4根号3-4根号2-8)/4
=根号6+根号3-根号2-2