# Prove identity

#### synergix

1. The problem statement, all variables and given/known data

Prove:
csc2@= 1/(1-(sin@-cos@)^2

2. Relevant equations

3. The attempt at a solution

I'm stuck cant seem to work this on out. I'm not seeing the relationship between the two

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#### synergix

I tried again and ended up with 1/sin2@=1/-sin2@

erg

#### HallsofIvy

On the right side, $(sin(\theta)- cos(\theta))^2= sin^2(\theta)- 2sin(\theta)cos(\theta)+ cos^2(\theta)$
$= 1- 2sin(\theta)cos(\theta)$
so $1- (sin(\theta)- cos(\theta))^2= 2sin(\theta)cos(\theta)$

Do you recognize that as $sin(2\theta)$?

#### synergix

mental error I got it

"Prove identity"

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