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.