sammietaygreen
  • sammietaygreen
Find cos(x) if sin^2 x-1/cos x = -1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
do you know that \[1-\sin^2(x)=\cos^2(x)\]?
sammietaygreen
  • sammietaygreen
no I am not sure
anonymous
  • anonymous
oh, well it does

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More answers

sammietaygreen
  • sammietaygreen
Oh I thought I had to solve for something. That is just a trig function sorry lol
anonymous
  • anonymous
the mother of all trig identities is \[\cos^2(x)+\sin^2(x)=1\] and all its cousins for example if you subtract \(\sin^2(x)\) you get \[1-\sin^2(x)=\cos^2(x)\]
anonymous
  • anonymous
you don't have \[1-\sin^2(x)\]you have \[\sin^2(x)-1\] which is the same as \[-\cos^2(x)\]
sammietaygreen
  • sammietaygreen
So you basically just have to simplify the trig function but not to a number?
anonymous
  • anonymous
you still have to solve the equation for \(x\)
anonymous
  • anonymous
but since the numerator is \(-\cos^2(x)\) it should be relatively easy
sammietaygreen
  • sammietaygreen
How do I solve for x? I have an idea but it's not like a normal equation
anonymous
  • anonymous
put \(-\cos^2(x)\) in the top, then cancel a cosine
sammietaygreen
  • sammietaygreen
on the top of what? like a fraction?
sammietaygreen
  • sammietaygreen
or set it equal to -1?
sammietaygreen
  • sammietaygreen
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
The original equation is this \[\Large \frac{\sin^2(x)-1}{\cos(x)} = -1\] right? or am I off?
jim_thompson5910
  • jim_thompson5910
OR is it this \[\Large \sin^2(x)-\frac{1}{\cos(x)} = -1\] @sammietaygreen
sammietaygreen
  • sammietaygreen
jim_thompson5910
  • jim_thompson5910
thanks
jim_thompson5910
  • jim_thompson5910
so as @satellite73 is saying, you'd follow these steps \[\Large \frac{\sin^2(x)-1}{\cos(x)} = -1\] \[\Large \frac{-\cos^2(x)}{\cos(x)} = -1\] \[\Large -\cos(x) = -1\] \[\Large \cos(x) = 1\]
sammietaygreen
  • sammietaygreen
so do I just solve x when it is simplified to cos(x) = 1
jim_thompson5910
  • jim_thompson5910
no need to solve for x itself they just want the value of `cos(x)`
sammietaygreen
  • sammietaygreen
Ohhh I get it now I don't know why I didn't understand before. So you just had to simplify it to get 1
jim_thompson5910
  • jim_thompson5910
yep 1 goes in the box
sammietaygreen
  • sammietaygreen
Okay. I just didn't understand what he was understanding about x but I get what you're saying. Thank you very much.

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