3.117
1)tgx=a
3a2+10a+3=0
D=100-36=64
a1=(-10-8)/6=-3⇒tgx=-3⇒x=-arctg3+πn
a2=(-10+8)/6=-1/3⇒tgx=-1/3⇒x=-arctg1/3+πn
4)ctg2x-(1-√3)ctg2x+√3-6=0
ctg2x=a
a²-(1-√3)a+√3-6=0
D=(1-√3)²-4(√3-6)=1-2√3+3-4√3+24=28-6√3
a1=(1-√3-√(28-6√3)/2⇒ctg2x=(1-√3-√(28-6√3)/2⇒x=1/2arcctg(1-√3-√(28-6√3)+πn/2
a2=(1-√3+√(28-6√3)/2⇒ctg2x=(1-√3+√(28-6√3)/2⇒x=1/2arcctg(1-√3+√(28-6√3)+πn/2
3.120
2)4-4sin²x-sinx-1=0
4sin²x+sinx-3=0
sinx=a
4a²+a-3=0
D=1+48=49
a1=(-1-7)/8=-1⇒sinx=-1⇒x=-π/2+2πn
a2=(-1+7)/8=3/4=0,75⇒sinx=0,75⇒x=(-1)^n*arcsin0,75+2πn