Question

Решите тригонометрическое неравенство.

Answer 1

1)  ctgx ≥ - 1
πn < x < arcctg(-1) + πn, n∈Z
πn < x < 3π/4 + πn, n∈Z
2) 2cos5x ≤ 1
 cos5x ≤ 1/2
arccos(1/2) + 2πk ≤ 5x ≤ 2π - arccos(1/2) + 2πk, k ∈Z
π/3 + 2πk ≤ 5x ≤ 2π - π/3 + 2πk, k ∈Z
π/3 + 2πk ≤ 5x ≤ 5π/3 + 2πk, k ∈Z
π/15 + 2πk/5 ≤ x ≤ π/3 + 2πk/5, k ∈Z