Question

2 sin(x) - 3 cos(x) = 2

Answer 1

Ответ:

2sinx-3cosx=2 4sin(x/2)cos(x/2)-3cos²(x/2)+3sin²(x/2)-2(cos²(x/2)+sin²(x/2))=0 4sin(x/2)cos(x/2)-5cos²(x/2)+sin²(x/2)=0 (:cos²(x/2)≠0) 4tg(x/2)-5+tg²(x/2)=0 tg²(x/2)+4tg(x/2)-5=0 tg(x/2)=y;y²+4y-5=0;y₁=-5;y₂=1 1) tg(x/2)=-5 x/2=arctg(-5)+πn x=-2arctg5+2πn,n∈Z 2) tg(x/2)=1 x/2=π/4+πk x=π/2+2πk,k∈Z