50 баллов!
17.ctg^2(2t-п/3)=3 18.tg^2(3x+П/2)=1/3
19. 3cos^2x-5cosx=0
20. знак модуля sin3x знак модуля =1/2

17)  ctq²(2x -π/3) =3;1+cos(4x -2π/3) =3(1-cos(4x- 2π/3) ;cos(4x - 2π/3) = 1/2 ;4x -2π/3 = π/3 +2π*k ;4x = π +2π*k;x₁ =π/4 +π/2*k  ,k∈ Z ;4x -2π/3 = - π/3 +2π*k ;4x  = π/3 +2π*k ;x₂=π/12 +π/2*k  , k∈ Z .18) tq²(3x+π/2) =1/3 ;ctq²3x =1/3 ;3(1+cos6x) =1-cos6x ;cos6x = -1/2 ;6x =  (+/-)(π -π/3) +2π*k ;x = (+/-)π/9 + π*k/3  ,  k∈ Z .19) 3cos²x -5cosx =0;3cosx(cosx -5/3) =0 ;cosx=0 ;x=π/2 +π*k , k∈ Z.cosx =5/3 >0. не имеет решения.20) |sin3x| =1/2;a) sin3x = -1/2; 3x₁  =(-1)^(k+1)*π/6 + π*k  , k∈ Z. x₁  =(-1)^(k+1)*π/18 + π/3*k , k∈ Z.b) sin3x = 1/2; 3x₂  =(-1)^k*π/6 + π*k  , k∈ Z.x₂  =(-1)^k*π/18 + π/3*k  , k∈ Z.