3sin²(x/2)+sin(x/2)*cos(x/2)-2sin²(x/2)-2cos²(x/2)=0
sin²(x/2)+sin(x/2)cos(x/2)-2cos²(x/2)=0 (/cos²x/2≠0
(sin(x/2)/cos(x/2))²+sin(x/2)/cos(x/2)-2=0
tg²x/2+tgx/2-2=0
tgx/2=t
t²+t-2=0
t=1 t=-2
tgx/2=1 tgx/2=-2
x/2=π/4+πn x/2=-arctg2+πn
x=π/2+2πn x=-2arctg2+2πn
Вот решение первого неравенства.
1)3xˇ2-12x=3x(x-4)
2)ab-2a+bˇ2-2b=a(b-2)+b(b-2)=(b-2)(a+b)
3)4xˇ2-9=(2x)ˇ2-3ˇ2=(2x+3)(2x-3)
4)xˇ3-8xˇ2+16x=x(xˇ2-8x+16)=x(x-4)(x-4)=x.(x-4)ˇ2