Need a trig explanation?

Here's what I did:

a) Rewrite equation to put one unknown (and i) on one side to get

cos(x) - sin(x) = i - i[sin(y)]

b) square both sides to get

cos^2(x) - 2(cos(x))(sin(x)) + sin^2(x) = i^2 - 2(i^2)(sin(y)) + i^2(sin^2(y))

c) substitute 1 for cos^2 + sin^2 on the left side; and i^2 = [sqrt(-1)]^2 or -1 on the right side to get

1 - 2(cos(x))(sin(x)) = -1 + 2(sin(y)) - 1(sin^2(y) = - (1 - sin(y))^2

d) multiply both sides of the equation by -1 and reverse left and right sides of equation to get

(1 - sin(y))^2 = 2(cos(x))(sin(x))

e) take sqrt of both sides to get 1 - sin(y) = sqrt[2(cos(x))(sin(x)]

f) subtract 1 from each side to get - sin(y) = sqrt[2(cos(x))(sin(x)] -1

g) divide both sides by -1 to get sin(y) = 1 - sqrt[2(cos(x))(sin(x)]

h) y = sin^-1 [1 - sqrt[2(cos(x))(sin(x)]

i) input above equation into graphing calculator and use trace function to input x values to get desired y values or manually input x values to get corresponding y values

equate real and imaginary parts

cosx = sinx; x = pi/4, pi+pi/4

siny = 1; y =pi/2