1 = sin(x) + cos(x)

1 = C/C (C ≠ 0) =>
1 = (1/C)*(C*sin(x) + C*cos(x)) =>
1 = (1/C)*(cos(a)*sin(x) + sin(a)*cos(x)) if C = sin(a) = cos(a)
=> 1 = tan(a)
=> a = π/4 as a possible solution
=> C = 1/sqrt(2)
=> 1 = sqrt(2)*(sin(x + π/4)) or 1/sqrt(2) = sin(x + π/4)