1. Выразить cos(a) через tg(a/2). 2. Дано tg a=2/3 (0

1) tg(a/2) = (1 - cosa)/sina;

tg(a/2) * sina = 1 - cosa;

tg(a/2) * sina - 1 = -cosa;

cosa = 1 - tg(a/2)sina;

2) tg2a = 2tga/(1 - tg^2a);

tg2a = 4/3/(1 - 4/9) = 4/3 : 5/9 = 4/3 * 9/5 = 12/5;

sin2a = 2tga/(1 + tg^2a) = 4/3 : (1 + 4/9) = 4/3 : 13/9 = 4/3 * 9/13 = 12/13;

cos2a = (1 - tg^2a)/(1 + tg^2a) = (1 - 4/9) : (1 + 4/9) = 5/9 : 13/9 = 5/9 * 9/13 = 5/13.