Question

Решите уравнение: sinx-cosx=1

Answer 1

Делим на √2:
1/√2 · sinx - 1/√2 · cosx = 1/√2
cos π/4 · sinx - sin π/4 · cosx = 1/√2
sin(x - π/4) = 1/√2
x - π/4 = π/4 + 2πn  или  x - π/4 = 3π/4 + 2πk
x = π/2 + 2πn                    x = π + 2πk