1.cos4x=корень из 3/2 2.sinx/2=-корень из 2/2 3. 2sin^2x+sinx-1=0 4. tg(x+П/6)=1/ корень из 3 5.4tgx+3ctgx=7

1 cos4x=√3/2 4x=+-π/6+2πn x=+-π/24+πn/2,n∈z 2 sinx/2=√2/2 x/2=(-1)^n*π/4+πn x=(-1)^n*π/2+2πn,n∈z 3 sinx=a 2a²+a-1=0 D=1+8=9 a1=(-1-3)/4=-1⇒sinx=-1⇒x=-π/2+2πn,n∈z a2=(-1+3)/4=1/2⇒sinx=1/2⇒x=(-1)^n*π/6+πn,n∈z 4 x+π/6=π/6+πn x=πn,n∈z 5 4tgx+3/tgx-7=0 4tg²x-7tgx+3=0,tgx≠0 tgx=a 4a²-7a+3=0 D=49-48=1 a1=(7-1)/8=3/4⇒tgx=3/4⇒x=arctg0,75+πn,n∈z a2=(1+7)/8=1⇒tgx=1⇒x=π/4+πn,n∈z