Question

sinA=.....+cosA

Answer 1

let sinA = x + cosA

x = sinA - cosA
x^2 = sin^2 A - 2sinAcosA + cos^2 A
x^2 = 1 - 2sinAcosA
x^2 = 1 - sin 2A
x = +/- sqrt(1-sin(2A)), |sin 2A| <= 1

not sure if that is what you want.

Since I squared the equation, any (A,x) would have to be verified