Question

Помогите с тригонометрией

Answer 1

sin^2(3x) - 2sin(6x) + cos^2(3x) = 0
sin^2(3x) - 2*(2*sin3x)*cos(3x) + cos^(3x) = 0   /cos^2(3x) ≠ 0
tg^2(3x) - 4tg(3x) + 1 = 0
D = 16 - 4*1*1 = 12
1)  tg(3x) = (4 - 2√3)/2 = 2 - √3
3x = arctg(2 - √3) + πn, n∈Z
x1 = (1/3)*arctg(2 - √3) + (πn)/3, n∈Z
2)   tg(3x) = (4 + 2√3)/2 = 2 +- √3
3x = arctg(2 + √3) + πn, n∈Z
x2 = (1/3)*arctg(2 + √3) + (πn)/3, n∈Z