Б) 7sin²x - 9sinxcosx + 6cos²x = 2
7sin²x - 9sinxcosx + 2 - 2sin²x + 4cos²x = 2
5sin²x - 9sinxcosx + 4cos²x = 0
5tg²x - 9tgx + 4 = 0
Пусть t = tgx.
D = 81 - 4•5•4 = 1
t1 = (9 + 1)/10 = 1
t2 = (9 - 1)/10 = 8/10 = 4/5
Обратная замена:
tgx = 1
x = π/4 + 2πn, n ∈ Z.
tgx = 4/5
x = arctg(4/5) + πn, n ∈ Z.
в) 2cos²(x/2) + cosx = 0
Воспользуемся формулой понижения степени:
2((1 + cosx)/2) + cosx = 0
1 + cosx + cosx = 0
2cosx = -1
cosx = -1/2
x = ± arccos(-1/2) + 2πn, n ∈ Z
x = ± 2π/3 + 2πn, n ∈ Z.