Question

решите уравнение sin2x+4cos²x=1

Answer 1

sin2x+4cos²x=1
2sinxcosx+4cos²x=sin²x+cos²x
sin²x-2sinxcosx-3cos²x=0 (:cos²x≠0)
tg²x-2tgx-3=0
tgx=y;y²-2y-3=0;y₁=-1;y₂=3
1) tgx=-1
x=-π/4+πn,n∈Z
2) tgx=3
x=arctg3+πk,k∈Z.