Verify that sin minus cos plus 1 divided by sin plus cos subtract 1 equals sin plus 1 divided by cos?

Answer 1

[sin - cos + 1]/[sin + cos - 1] = [sin + 1]/cosiff [sin - cos + 1]*cos = [sin + 1]*[sin + cos - 1]
iff sin*cos - cos^2 + cos = sin^2 + sin*cos - sin + sin + cos - 1

iff -cos^2 = sin^2 - 1

1 = sin^2 + cos^2, which is true,