2/tg²x-1/sinx -4=0
2cos²x/sin²x -1/sinx -4=0
2cos²x-sinx-4sin²x=0,sinx≠0
2-2sin²x-sinx-4sin²x=0
6sin²x+sinx-2=0
sinx=t
6t²+t-2=0
D=1+48=49
t1=(-1-7)/12=-2/3⇒sinx=-2/3
x=-arcsin2/3+2πk,k∈z x=-arcsin2/3∈[-π/2;π/2]
x=-π+arcsin2/3+2πk нет решения на [-π/2;π/2]
t2=(-1+7)/12=1/2⇒sinx=1/2
x=π/6+2πk,k∈z x=π/6∈[-π/2;π/2]
x=5π/6+2πk,k∈z нет решения на [-π/2;π/2]