Question

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

Answer 1

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