1)tg² x = 3
tg x = √3 или tg x = -√3
x = arctg √3 + πn, n∈ Z x = arctg(-√3) + πk, k∈Z
x = π/3 + πn, n∈Z x = -π/3 + πk, k∈Z
Ответ: π/3 + πn, n∈Z; -π/3 + πk, k∈Z
2)ctg²x = 1/3
ctg x = √3/3 или ctg x = -√3/3
x = arcctg √3/3 + πn,n∈Z x = arcctg(-√3/3) + πk, k∈Z
x = π/3 + πn, n∈Z x = 2π/3 + πk, k∈Z
Ответ: π/3 + πn, n∈Z ; 2π/3 + πk, k∈Z.
3)cos²x = 3/4
cos x = √3/2 или cos x = -√3/2
x = ±arccos √3/2 + 2πn, n∈Z x = ±arccos(-√3/2) + 2πk,k∈Z
x = ±π/6 + 2πn, n∈ Z x = ±5π/6 + 2πk,k∈Z
Ответ: ±π/6 + 2πn, n∈ Z; ±5π/6 + 2πk,k∈Z
4)sin²x = 1/2
sin x = √2/2 или sin x = -√2/2
x = (-1)^k * arcsin √2/2 + πn, n∈Z x = (-1)^k * arcsin(-√2/2)+πk
x = (-1)^k * π/4 + πn, n∈Z x = (-1)^k+1 * π/4 + πk,k∈Z
Ответ:(-1)^k * π/4 + πn, n∈Z; (-1)^k+1 * π/4 + πk,k∈Z
5)|tg x| = 4
tg x = -4 или tg x = 4
x = arctg (-4) + πn,n∈Z x = arctg 4 + πk, k∈Z
x = -arctg 4 + πn, n∈Z
Ответ: -arctg 4 + πn, n∈Z; arctg 4 + πk, k∈Z