ОДЗ
cos3x≠0⇒3x≠π/2+πk⇒x≠π/6+πk/3
4sin3x+1-9cos3x=0
8sin(3x/2)cos(3x/2)+sin²(3x/2)+cos²(3x/2)-9cos²(3x/2)+9sin²(3x/2)=0
8sin(3x/2)cos(3x/2)+10sin²(3x/2)-8cos²(3x/2)=0/cos²(3x/2)
10tg²(3x/2)+8tg(3x/2)-8=0
tg(3x/2)=a
10a²+8a-8=0
5a²+4a-4=0
d=16+80=96
a1=(-4-4√6)/10=-0,4-0,4√6⇒tg(3x/2)=-0,4-0,4√6⇒
3x/2=-arctg(0,4+0,4√6)+πk⇒x=-2/3*acrtg(0,4+0,4√6)+2πk/2,k∈z
a2=-0,4+0,4√6⇒tg(3x/2)=-0,4+0,4√6⇒
3x/2=-arctg(0,4-0,4√6)+πk⇒x=-2/3*acrtg(0,4-0,4√6)+2πk/2,k∈z