Question

Помогите решить sin x+ cos x= 1+ sin x* cos x

Answer 1

sin(x) + cos(x) = 1 + sin(x)*cos(x),

sin(x)*cos(x) - sin(x) - cos(x) + 1 = 0,

sin(x)*( cos(x) - 1 ) - ( cos(x) - 1 ) = 0,

( cos(x) - 1 )*( sin(x) - 1 ) = 0,

cos(x) - 1 = 0 или sin(x) - 1 = 0,

cos(x) = 1 или sin(x) = 1,

x = 2πn, n∈Z или x = (π/2) + 2πk, k∈Z.