a)

б)

в)

a). sinx+√3cosx=0 |:cosx≠0
tgx+√3=0, tgx=-√3
x=arctg(-√3)+πn, n∈Z
x=-π/3+πn, n∈Z
б). sin²x+2sinx*cosx-3cos²x=0 |: cos²x≠0
tg²x+2tgx-3=0, tgx=y
y²+2y-3=0
y₁=-3,  tgx=-3, x₁=-arctg3+πn, n∈Z
y₂=1, tgx=1,    x₂=π/4+πn, n∈Z
в). sin²x-4sinx*cosx+3cos²x=0 |: cos²x≠0
tg²x-4tgx+3=0, tgx=y
y²-4y+3=0
y₁=1, tgx=1,   x₁=π/4+πn, n∈Z
y₂=3, tgx=3,   x₂=arctg3+πn, n∈Z