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