Proving Trig Identity

Question

I'm having trouble trying to prove this trig identity. Help is greatly appreciated. Thanks in advance.

1/(csc-cot) = (1+cos)/sin

Answer 1

1/(csc-cot)=(1+cos)/sin

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

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

sin/(1-cos)

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

(sin)(1+cos)/(1-cos²)

(sin)(1+cos)/sin²

(1+cos)/sin which is the right side