1a)4(1-cos²x)+4cosx-1=04-4cos²x+4cosx-1=0cosx=a4a²-4a-3=0D=16+48=64a1=(4-8)/8=-1/2⇒cosx=-1/2⇒x=+-2π/3+2πn,n∈za2=(4+8)/8=1,5⇒cosx=1,5>1 нет решенияб)sinx*(√3sinx+cosx)=0sinx=0⇒x=πn,n∈z√3sinx+cosx=0/cosx√3tgx+1=0⇒tgx=-1/√3⇒x=-π/6+πk,k∈z2tgx=a3a²-4√3a+3<0D=48-36=12a1=(4√3-2√3)/6=√3/2a2=(4√3+2√3)/6=√3√3/3<a<√3⇒√3/3<tgx<√3⇒π/6+πn<x<π/3+πn,n∈z3sinxcosx-5sin²x+3sin²x+3cos²x=02sin²x-sinxcosx-3cos²x=0/cos²x2tg²x-tgx-3=0tgx=a2a²-a-3=0D=1+24=25a1=(1-5)/4=-1⇒tgx=-1⇒x=-π/4+πn,n∈z-π/2<-π/4+πn<π-2<-1+4n<4-1<4n<5-1/4<n<5/4n=0⇒x=-π/4n=1⇒x=-π/4+π=3π/4a2=(1+5)/4=1,5⇒tgx=1,5⇒x=arctg1,5+πk,k∈z-π/2<arctg1,5+πk<π нет решения4{xcos6y=5⇒x=5/cos6y{xsin6y=-55sin6y/cos6y=-5tg6y=-16y=-π/4y=-π/24x=5/cos(-π/24)=5/cos24≈5/0,9≈5,6