Question

Помогите решить
$1- sinx+cosx=0$

Answer 1

cosx - sinx + 1 = 0
cos(2*x/2) = cos^2(x/2) - sin^2(x/2)
sin(2*x/2) = 2sin(x/2)*cos(x/2)
1 = cos^2(x/2) + sin^2(x/2)
cos^2(x/2) - sin^2(x/2) - 2sin(x/2)*cos(x/2) + cos^2(x/2) + sin^2(x/2) = 0
2cos^2(x/2) - 2sin(x/2)*cos(x/2) = 0
2cos(x/2)*(cos(x/2) - sin(x/2)) = 0
1) cos(x/2) = 0
x/2 = π/2 + πk
x = π + 2πk
2) cos(x/2) - sin(x/2) = 0
sin(x/2) = cos(x/2)
tg(x/2) = 1
x/2 = π/4 + πk
x = π/2 + 2πk