4sin²x=tgx. 4sin²x-tgx=0. 4sin²x-sinx/cosx=0
(4sin²xcosx-sinx)/cosx=0
sinx*(4sinxcosx-1)/cosx=0
(sinx/cosx)*(2*(2sinxcosx)-1)=0
tgx*(2sin2x-1)=0
tgx=0 или 2sin2x-1=0
1. tgx=0. x₁=πn, n∈Z
2. 2sin2x=1, sin2x=1/2. 2x=(-1)^n *arcsin(1/2)+πn, n∈Z
2x=(-1)^n *(π/6)+πn, n∈Z |: 2
x₂=(-1)^n *(π/12)+πn/2, n∈Z