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

[synergix]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

 

[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