2) a) tga = 3 = sina/cosa = sqrt(1 - cos^2(a)) / cosa
sqrt(1 - cos^2(a)) = 3cosa
в 1 четверти синус и косинус положительны, значит можно обе части возвести в квадрат
1 - cos^2(a) = 9cos^2(a)
cos^2(a) = 1/10, cos(a) = √10/10
b) ctg(a) = cos(a)/sin(a) = 5/13 / 12/13 = 5/12
sin(a) = 12/13, cos(a) = sqrt(1 - 144/169) = 5/13
3) a) (cosx*(1 + sinx) + cosx*(1 - sinx)) / (1 - sin^2(x)) = (cosx + cosx*sinx + cosx - sinx*cosx) / cos^2(x) = 2cosx/cos^2(x) = 2/cosx
b) (tg^2(y) - 1 + cos^2(y)*sin^2(y)/cos^2(y) + cos^2(y)) / (tg^2(y) + 1) = tg^2(y) / (tg^2(y) + 1) = sin^2(y)*cos^2(y)/cos^2(y) = sin^2(y)
4) sin(a) = 8/17, cosa = +-sqrt(225/289) = +- 15/17, tga = +- 8/15, ctga = +- 15/8