2) формула: тангенс половинного аргумента tg (a/2) = (1 - cosa) / sina
(tg(п/4 - a))^2 = (1 - cos(п/2 - 2a))^2 / (sin(п/2 - 2a))^2 = (1 - sin2a)^2 / (cos2a)^2 =
(1 - sin2a)^2 / (1 - (sin2a)^2) = (1 - 1/3)^2 / (1 - (1/3)^2) = 4/9 : 8/9 = 4/9 * 9/8 = 4/8 = 1/2
1) a) в числителе синус двойного аргумента, в знаменателе осн.триг.тождество
...= (sin(2п/5))^2 / 4 * ((1 - (cos(2п/5))^2)*(1 + (cos(2п/5))^2) - (sin(2п/5))^2*(cos(2п/5))^2) =
(sin(2п/5))^2 / 4 * ((sin(2п/5))^2*(1 + (cos(2п/5))^2) - (sin(2п/5))^2*(cos(2п/5))^2) =
(sin(2п/5))^2 / 4 * ((sin(2п/5))^2 + (sin(2п/5))^2*(cos(2п/5))^2 - (sin(2п/5))^2*(cos(2п/5))^2) =
(sin(2п/5))^2 / 4 * (sin(2п/5))^2 = 1/4