Решить неравенство 4sin(x/2) * cos(x/2) ≤ -1

Question

Решить неравенство

4sin(x/2) * cos(x/2) ≤ -1

Answer 1

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

2sinx<=-1</p>

sinx<=-1/2</p>

sinx=-1/2  x=-П/6+2Пk

                 x=-5/6П+2Пk

ответ -5/6П+2Пk<=x<=-П/6+2Пk</p>

         

 

Answer 2

4sin(x/2) * cos(x/2) ≤ -1 

2sin(x)<=-1</p>

sin(x)<=-1/2</p>

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>