Tg3x=1 sin(x+pi/6)=-1 2cos^2x+cosx-1=0 тригонометрические уравнения

Tg3x=1
3x=Pi/4+Pi*n
x=3Pi/4+Pi/3*n

sin(x+Pi/6)=-1
x+Pi/6=-Pi/2+2Pi*n
x=-Pi/6-Pi/2+2Pi*n
x=-2Pi/3+2Pi*n

2Cos^2x+Cosx-1=0; Cosx=a a=/=0
2a^2+a-1=0
d=9
a=(-1+-3)/4
a1=-1; a2=1/2
Cosx=-1 Cosx=1/2
x=-Pi+2Pi*n x=+-Pi/3+2Pi*n

1)
tg3x = 1 
3x = pi/4 + pik, k∈Z
x = pi/12 + pik/3, k∈Z

2)
sin(x+pi/6) = -1
x+pi/6 = - pi/2 + 2pik
x = -pi/2 - pi/6 + 2pik, k∈Z

3)
2cos²x + cosx -1 = 0
cosx = t
2t² + t - 1 = 0
D= b²-4*a*c  = 1 - (-4*2*1) = 9   √D = 3
t1 = (-1+3)/4 = 1/2
t2 = (-1-3)/4 = -1

cosx = 1/2
x = (+-) pi/3 + 2pik, k ∈ Z

cosx = -1
x = pi + 2pik, k ∈ Z