Question

(1-ctg x) / (sin x - cos x)

Answer 1

$frac{1-ctg x}{sin x - cos x} = frac{1- frac{cosx}{sinx} }{sin x - cos x} = frac{ frac{sinx-cosx}{sinx} }{sin x - cos x} = frac{sinx-cosx }{sinx(sin x - cos x)} = frac{1}{sinx}$