1/1-sin = cot/cot - cos? pls prove?

Question

1/1-sin = cot/cot - cos? pls prove?

Answer 1

You mean 1/(1-Sin x)=Cot x/(Cot x - Cos x),then inverse them,you get

1- Sin x=1-(Cos x/Cot x)=1- Cos x/Cos x/Sin x=1-Sin x Cos x/Cos x=

1- Sin x

Answer 2

cot = 1/sin

so cot/ cot- cos = (1/sin) / ( 1/sin - cos) = (1/sin) / [(1- sin cos) / sin]

= 1/ 1-sincos

Answer 3

divide numerator and denominator by cot.