Question

 Решить неравенство

 

4sin(x/2) * cos(x/2) ≤ -1  

Answer 1

4sin(x/2) * cos(x/2) ≤ -1 

2sin(x)<=-1

sin(x)<=-1/2

sin(x)=-1/2

x=(-1)^n*arcsin(-1/2)+pi*n

(-1)^n*arcsin(-1/2)+pi*n <=x <= (-1)^(n+1)*arcsin(-1/2)+pi*n>

 

Answer 2

4sin(x/2)*cos(x/2)<=-1

2sinx<=-1

sinx<=-1/2

sinx=-1/2  x=-П/6+2Пk

                 x=-5/6П+2Пk

ответ -5/6П+2Пk<=x<=-П/6+2Пk