1. 2 cos квадрат x - 5 sin x + 1

1.
2-2sinx^2 - 5sinx+1 = 0
2sinx^2 + 5sinx -3 = 0
sinx = t, t 1,
2t^2 +5t - 3 =0
D = 25+4*2*3 = 25+24 = 49
D = 7
t1 =(-5-7)/4=-3
t2 =(-5+7)/4=1/2
sinx=1/2
x = (-1)^k*/6+k, kZ
2.
1 - 2sinx^2 -sinx = 0
2sinx^2 + sinx -1 =0
sinx = t, t 1,
2t^2 +t - 1 =0
D=1+4*2*1=9
D = 3
sinx=(-1-3)/4=-1
x =-/2+2k, kZ
sinx=(-1+3)/4=1/2
x = (-1)^k*/6+k, kZ
3.
sin2x=0
2x=k, kZ
x=k/2, kZ
4.
sin2x+ sin x = 0
2sinx*cosx+ sin x = 0
sinx(2cosx+1)=0
sinx=0, x=k, kZ,
cosx=-1/2, x=2/3+2k, kZ