4cos²x+sin x-1=0;
4(1-sin²x)+sin x-1=0;
4-4sin²x+sin x-1=0;
-4sin²x+sin x+3=0;
4sin²x-sin x-3=0;
sin x=t, -1≤t≤1;
4t²-t-3=0;
D=49;
t1=-3/4;
t2=1;
sin x=-3/4 или sin x=1;
x=(-1)^k*arcsin(-3/4)+πk, k∈Z; x=π/2+2πn, n∈Z.
x=(-1)^(k+1)*arcsin(3/4)+πk, k∈Z.
Ответ: (-1)^(k+1)*arcsin(3/4)+πk, k∈Z; π/2+2πn, n∈Z.