Решите уравнения:

а) cos (x/2 + π/4) + 1 = 0

б) 2cos π/6 * tgx * ctgx = 0

Решение

а) cos (x/2 + π/4) + 1 = 0

cos (x/2 + π/4) = - 1

x/2 + π/4 = π + 2πk, k∈Z

x/2 = π - π/4 + 2πk, k∈Z

x/2 = 3π/4 + 2πk, k∈Z

x = 3π/2 + 4πk, k∈Z

б) 2cos π/6 * tgx * ctgx = 0

2 * (√3/2) * tgx * ctgx = 0

tgx * ctgx = 0

tgx = 0

x = πn, n∈Z

ctgx = 0

x = π/2 + πk, k∈Z