1)tg(a+b),если tga=1/5,tgb=2/3 2)ctg(a-b),если tga=3/2,tgb=5/2 3)tg(п/4+a,если sina=12/13 a(принадлежит) (п/2,п)

1) tg(a + b) = (tga + tgb)/(1 - tgatgb) = (1/5 + 2/3)/(1 - 1/5 * 2/3) = 13/15/13/15 = 1;

 tga = 3/2, tgb = 5/2;

2) ctg(a - b) = (2/3 * 2/5 + 1)/(2/3 - 2/5) = (4/15 + 15/15)/(4/15) = 19/15 : 4/15 = 19/15 * 15/4 = 19/4 = 4,75;

ctga = 2/3, ctgb = 2/5;

3) tg(п/4 + a)  = (tgп/4 + tga)/(1 - tgп/4tga) = (1 + tga)/(1 - tga);

sina = 12/13 a (принадлежит) (п/2,п);

tga = sina/cosa;

sin^2a + cos^2a = 1;

cos^2a = 1 - sin^2a;

cos^2a = 1 - 144/169;

cos^2a = 25/169;

cosa = +-5/13;

cosa = -5/13 - вторая четверть;

tga = 12/13 : (-5/13) = 12/13 * (-13/5) = -12/5 = -2,4;

(1 + tga)/(1 - tga) = (1 -2,4)/(1 + 2,4) = -1,4/3,4 = -14/34.

tg(п/4 + a) = -14/34.