some help..please.

[Danielle058]

Proving this is an identity;

(1+sin(theta)/(sin(theta)=(Cot^2 (theta)/(csc (theta)-1)

I cross multiplied and used FOIL to get: csc(theta)-sin(theta)= sin(theta) times (cot^2 theta)

..Is that right? Where do I go from there? (Because I can't find a way to prove it) :?

 

[ChaoticLlama]

(1+sin(Θ)/(sin(Θ) = (cot²(Θ)/(csc (Θ)-1)

csc(Θ) + 1 = (cot²(Θ)/(csc (Θ)-1)

(csc(Θ) + 1)(csc (Θ) - 1) = (cot²(Θ))

csc²(Θ) - 1 = cot²(Θ)

QED