алгебра 10 класс, пожалуйста помогите

№ 1. Тангенс разности
tg (4x - y) = (tg (4x) - tg y) / (1 + tg (4x) * tg y)
Тангенс двойного угла
tg (2x) = 2tg x / (1 - tg^2 x)
tg (4x) = 2tg (2x) / (1 - tg^2 (2x)) = 2*2tg x / (1 - tg^2 x) : (1 - [2tg x / (1 - tg^2 x)]^2) =
= 4tg x / (1 - tg^2 x) : ( 1 - [4tg^2 x / (1 - tg^2 x)^2] ) = 4tg x / (1 - tg^2 x) : ((1 - tg^2 x)^2 - 4tg^2 x) / (1 - tg^2 x)^2 =
= 4tg x / (1 - tg^2 x) * (1 - tg^2 x)^2 / ((1 - tg^2 x)^2 - 4tg^2 x) = 4tg x / (1 - tg^2 x) * (1 - tg^2 x)^2 / (1 - 2tg^2 x + tg^4 x - 4tg^2 x) =
= [4tg x * (1 - tg^2 x)^2 ] / [ (1 - tg^2 x) * (1 - 6tg^2 x + tg^4 x)] = [4tg x * (1 - tg^2 x)] / (1 - 6tg^2 x + tg^4 x) =
= (4tg x - 4tg^3 x) / (1 - 6tg^2 x + tg^4 x) = (4/5 - 4/125) : (1 - 6/25 + 1/625) = 96/25 : 476/625 = 96 * 25 / 476 = 600 / 119
Подставляем найденное в формулу:
tg (4x - y) = (tg (4x)-tg y) / (1+tg (4x)*tg y) = (600/119 - 1/239) : (1 + 600/119/239) = (600*239-119)/239 : (119*239 + 600)/(119*239) =
= 143281/239 : 29041/(119*239) = 143281*119/29041 = 17050439/29041 ~ 587,116

№ 2. Формулы половинного аргумента
sin^2 (a/2) = (1 - cos a) / 2, cos^2 (a/2) = (1 + cos a) / 2, tg (a/2) = sin (a/2) / cos (a/2)
1) a = 30*, a/2 = 15*
sin^2 (15) = (1 - cos 30) / 2 = (1 - V(3)/2) / 2 = (2 - V(3)) / 4
sin (15) = V(2 - V(3)) / 2
cos^2 (15) = (1 + cos 30) / 2 = (1 + V(3)/2) / 2 = (2 + V(3)) / 4
cos (15) = V(2 + V(3)) / 2
tg (15) = [V(2 - V(3)) / 2] : [V(2 + V(3)) / 2] = [V(2 - V(3))] : [V(2 + V(3))] = [V(2 - V(3))]^2 : [V(2 + V(3))*V(2 - V(3))] =
= (2 - V(3)) : V[(2 + V(3))*(2 - V(3))] = (2 - V(3)) : V(4 - 3) = (2 - V(3)) / 1 = 2 - V(3)
2) a = Pi/4, a/2 = Pi/8
sin^2 (Pi/8) = (1 - cos Pi/4) / 2 = (1 - V(2)/2) / 2 = (2 - V(2)) / 4
sin (Pi/8) = V(2 - V(2)) / 2
cos^2 (Pi/8) = (1 + cos Pi/4) / 2 = (1 + V(2)/2) / 2 = (2 + V(2)) / 4
cos (Pi/8) = V(2 + V(2)) / 2
tg (Pi/8) = [V(2 - V(2)) / 2] : [V(2 + V(2)) / 2] = [V(2 - V(2))] : [V(2 + V(2))] = [V(2 - V(2))]^2 : [V(2 + V(2))*V(2 - V(2))] =
= (2 - V(2)) : V[(2 + V(2))*(2 - V(2))] = (2 - V(2)) : V(4 - 2) = (2 - V(2)) / V(2) = V(2) - 1
3) cos a = 0,6
sin^2 (a/2) = (1 - cos a) / 2 = (1 - 0,6) / 2 = 0,4 / 2 = 0,2
sin (a/2) = V(0,2)
cos^2 (a/2) = (1 + cos a) / 2 = (1 + 0,6) / 2 = 1,6 / 2 = 0,8
cos (a/2) = V(0,8) = V(4*0,2) = 2V(0,2)
tg (a/2) = sin (a/2) / cos (a/2) = V(0,2) / 2V(0,2) = 1/2

№1. sin x = 0,96; 0 < x < Pi/2
cos x = V(1 - sin^2 x) = V(1 - 0,96^2) = V(0,0784) = 0,28
sin 2x = 2 * sin x * cos x = 2 * 0,96 * 0,28 = 0,5376
cos 2x = cos^2 x - sin^2 x = 0,28^2 - 0,96^2 = 0,0784 - 0,9216 = - 0,8432
tg 2x = sin 2x / cos 2x = 0,5376 / (- 0,8432) ~ - 0,6376

№2. tg x = -2.
tg 2x = 2tg x / (1 - tg^2 x) = -2 * 2 / (1 - 4) = -4 / (-3) = 4/3

№3. ctg x = 2, tg x = 1/2
Формулы функций, выраженные через тангенс половинного угла.
sin 2x = 2tg x / (1 + tg^2 x) = 2*1/2 : (1 + 1/4) = 1 : 5/4 = 4/5
cos 2x = (1 - tg^2 x) / (1 + tg^2 x) = (1 - 1/4) : (1 + 1/4) = 3/4 : 5/4 = 3/5
tg 2x = sin 2x / cos 2x = 4/5 : 3/5 = 4/3

sin 4x = 2tg (2x) / (1 + tg^2 (2x)) = 2*4/3 : (1 + 16/9) = 8/3 : 25/9 = 8/3 * 9/25 = 8*3/25 = 24/25
cos 4x = (1 - tg^2 (2x)) / (1 + tg^2 (2x)) = (1 - 16/9) : (1 + 16/9) = -7/9 : 25/9 = -7/25
tg 4x = sin 4x / cos 4x = 24/25 : (-7/25) = -24/7

№4 Первый замечательный предел: lim (x -> 0) (sin x / x) = 1
Решаем:
lim (x -> 0) (tg x / x) = lim (x -> 0) (sin x / (cos x * x)) = lim (x -> 0) (sin x / x) * lim (x -> 0) (1 / cos x) = 1 * 1/cos 0 = 1
lim (x -> 0) (tg 2x / 3x) = lim (x -> 0) (tg 2x / 2x) * 2/3 = 1 * 2/3 = 2/3 (смотри предыдущий пример)
lim (x -> 0) (tg x * 5x / tg 7x) = lim (x -> 0) (tg x * 7x / tg 7x) * 5/7 = lim (x -> 0) (tg x) * lim (x -> 0) (7x / tg 7x) * 5/7 = 0 * 1 * 5/7 = 0

тангенс разности
1) tg (4x - y) = tg (1/5 - 1/239) = tg (239 - 5) / (5*239) = tg 234 / 1195 ~ tg 0,195

2) sin^2 (a/2) = (1 - cos a) / 2 = (1 - cos 30) / 2 = (1 - V(3)/2) / 2 = (2 - V(3)) / 4
sin (15) = V(2 - V(3)) / 2
cos (15) = V(2 + V(3)) / 2
tg (15) = V(2 - V(3)) / V(2 + V(3))