1. 2cos2x=7cosx

2. cos^4x-sin^4x=sqrt (3) / 2

3. sin^2x-sqrt (3) / 2*sin2x=cos^2x

1) 2 (2cos²x-1) - 7cosx=0

4cos²x-7cosx-2=0

a=cosx 4a²-7a-2=0 D=49+32=81 √D=9

a1 = (7-9) / 8=-1/4 cosx=-1/4 x=π + - arccos1/4+2πn

a2 = (7+9) / 8=2∉[-1; 1]-нет решения

2) (cos²x-sin²x) (cos²x+sin²x) = √3/2

cos2x=√3/2

2x = + - π/6+2πn⇒x = + - π/12+πn

3) cos²x-sin²x+√3/2sin2x=0

cos2x-√3/2sin2x=0 / cos2x≠0

1-√3/2tg2x=0

tg2x=2/√3=2√3/3

2x=arctg2√3/3+πn

x=1/2arctg2√3/3+πn/2