Question

Решите уравнение: cosx^2-sinx^2=-1/2

Answer 1

Сos x² - Cos(π/2 - x²) = -1/2
-2Sinπ/4·Sin(-π/4 + x²) = -1/2
-2·1/√2Sin(x² - π/4) = -1/2
Sin(x² - π/4) = √2/4
х² - π/4 = (-1)^n arcSin(√2/4) + nπ, n∈Z
x² = (-1)^n arcSin(√2/4) + nπ + π/4 , n∈Z
x = +-√((-1)^n arcSin(√2/4) + nπ + π/4), n∈2k, k ∈Z