How do you show that 2 sin squared x minus 1 divided by sin x minus cos x equals sin x plus cos x?

Answer 1

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

(sin^2 x + sin^2 x - 1)/(sin x - cos x) =? sin x + cos x

[sin^2 x - (1 - sin^2 x)]/(sin x - cos x) =? sin x + cos x

(sin^2 x - cos^2 x)/(sin x - cos x) =? sin x + cos x

[(sin x - cos x)(sin x + cos x)]/(sin x - cos x) =? sin x + cos x

sin x + cos x = sin x + cos x