Question

Решите уравнение
sinx-cosx=1

Answer 1

sinx - cosx = 1
делим на √2
1/√2sinx - 1/√2cosx = 1/√2
sinx·cos(π/4) - cosx·sin(π/4) = 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