Sinx = -(cos^2(x/2) - sin^2(x/2)) - справа формула косинуса двойного угла
sinx = -cosx - разделим обе части на cosx
tgx = -1
x = -π/4 + πk, k∈Z
x∈[-2π; 11π/4]
-2π ≤ -π/4 + πk ≤ 11π/4
-2π + π/4 ≤ πk ≤ 11π/4 + π/4
-7/4 ≤ k ≤ 3, k∈Z
k = -1, 0, 1, 2, 3
k = -1, x = -π/4 - π = -5π/4
k = 0, x = -π/4
k = 1, x = -π/4 + π = 3π/4
k = 2, x = -π/4 + 2π = 7π/4
k = 3, x = -π/4 + 3π = 11π/4
Ответ: -5π/4, -π/4, 3π/4, 7π/4, 11π/4