Prove identity

  • Thread starter synergix
  • Start date
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
 
I tried again and ended up with 1/sin2@=1/-sin2@

erg
 

HallsofIvy

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On the right side, [itex](sin(\theta)- cos(\theta))^2= sin^2(\theta)- 2sin(\theta)cos(\theta)+ cos^2(\theta)[/itex]
[itex]= 1- 2sin(\theta)cos(\theta)[/itex]
so [itex]1- (sin(\theta)- cos(\theta))^2= 2sin(\theta)cos(\theta)[/itex]

Do you recognize that as [itex]sin(2\theta)[/itex]?
 
mental error I got it
 

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