Question

cum se calculeaza tg 75

Answer 1

Folosesti formula tg(x+y) = (tgx + tgy)/(1-tgx*tgy)

tg75° = tg(30° + 45°) = (tg30° + tg45°)/(1-tg30°*tg45°) = ((√3)/3 + 1)/(1- (√3)/3)=((3+√3)/3)/((3-√3)/3)=(3+√3)/(3-√3)

Amplifici ultima fractie cu (3+√3) (rationalizezi numitorul)
tg75° = (3+√3)²/(9-3) = (12+6√3)/6 = 2+√3

Deci, tg75° = 2+√3