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)