how do you prove the identity csc(x)-cot(x)=sin(x)/1+cos(x)

Answer 1

csc(x) - cot(x) =

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

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

1-cos(x)/sin(x) * (1 + cos(x))/(1 + cos(x)) =

(1 - cos²(x))/(sin(x)(1+cos(x)) =

sin²(x)/(sin(x)(1+cos(x)) =

sin(x)/(1+cos(x))