Решите уравнения а) cos ( x/2 + π/4 ) + 1 = 0 б) - вопрос №2410264608445 от stepazhdanov2 25.01.2021 07:03

Question

Алгебра: Решите уравнения а) cos ( x/2 + π/4 ) + 1 = 0 б) 2cos π/6 * tgx * ctgx = 0 в) cos (-x) = √3/2

stepazhdanov2 · Answer

Решениеа) cos ( x/2 + π/4 ) + 1 = 0cos ( x/2 + π/4 )  = - 1x/2 + π/4 = π + 2πk, k∈Zx/2 = π - π/4 + 2πk, k∈Zx/2 = 3π/4 + 2πk, k∈Zx = 3π/2 + 4πk, k∈Zб) 2cos π/6 * tgx * ctgx = 02*(√3/2) * tgx * ctgx = 0 tgx * ctgx = 0tgx  = 0x = πn, n∈Zctgx = 0x = π/2 + πk, k∈Zв) cos (-x) = √3/2cosx = √3/2x = (+ -)arccos(√3/2) + 2πm, m∈Zx = (+ -)*(π/6) + 2πm, m∈Z...