anonymous
  • anonymous
Simplify the expression: Sin^2x-1/cos(-x)
Mathematics
katieb
  • katieb
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SolomonZelman
  • SolomonZelman
Have you seen the following identity? \(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta=1 }\)
anonymous
  • anonymous
Yes
SolomonZelman
  • SolomonZelman
Subtract \(\sin^2\theta\) from both sides and tell me what you get.

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SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta =1 \ }\) \(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta \color{blue}{-\sin^2\theta }=1 \color{blue}{-\sin^2\theta } }\) \(\large\color{black}{ \displaystyle \cos^2\theta =1-\sin^2\theta }\)
SolomonZelman
  • SolomonZelman
So, based on the very last statement, you can now simplify your expression: \(\large\color{black}{ \displaystyle \frac{1-\sin^2x}{\cos x} =\frac{?}{\cos x} }\)
SolomonZelman
  • SolomonZelman
hello?
anonymous
  • anonymous
Sinx?
SolomonZelman
  • SolomonZelman
We have concluded that: \(1-\sin^2\theta =\cos^2\theta\) correct?
anonymous
  • anonymous
Yes so the ? Represents cos^2 theta?
SolomonZelman
  • SolomonZelman
Yes, therefore it comes out that: \(\large\color{black}{ \displaystyle \frac{1-\sin^2x}{\cos x} =\frac{\cos^2x}{\cos x} }\)
SolomonZelman
  • SolomonZelman
and THAT \(\Uparrow\) you can probably tell me how to simplify:D
anonymous
  • anonymous
So the answer is cos x? :)
SolomonZelman
  • SolomonZelman
yes, just \(\cos x\).
SolomonZelman
  • SolomonZelman
Any questions?
anonymous
  • anonymous
Thank you for your help! i understand it now :D
SolomonZelman
  • SolomonZelman
Yes, one more note: \(\color{red}{\cos(-\theta)=\cos(\theta)}\)
SolomonZelman
  • SolomonZelman
So, lets quicly recap everything once more, okay?
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle \frac{1-\sin^2(x)}{\cos (-x)} = }\) \(\large\color{black}{ \displaystyle \frac{1-\sin^2(x)}{\cos (x)} = }\) \(\large\color{black}{ \displaystyle \frac{\cos^2(x)}{\cos (x)} = \cos(x) }\)

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