If sinx+cosx=sqrt(2)sin(x+Aπ), then the number 0<A=___________ <2

Question

please provide all steps for the solution

Answer 1

sinx + cosx = √2[(1/√2)sinx + (1/√2)cosx)]

= √2[cos(π/4)sinx + sin(π/4)cosx] = √2sin(x + π/4) = √2sin[x + (1/4)π]

A = 1/4