Madgirlwithabluebox
  • Madgirlwithabluebox
Simplify the trigonometric expression. (will medal)
Mathematics
schrodinger
  • schrodinger
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Madgirlwithabluebox
  • Madgirlwithabluebox
\[ \frac{ \sin^2\theta}{ 1+\cos \theta}\]
freckles
  • freckles
sin^2(theta) can be written as 1-cos^2(theta) and guess what that can be factored
mathstudent55
  • mathstudent55
Use the identity below (solved for \(\sin^2 \theta\)) \(\sin^2 \theta + \cos^2 \theta = 1\) and do a substitution in the numerator. Then factor the numerator and reduce.

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Madgirlwithabluebox
  • Madgirlwithabluebox
Im still really confused
anonymous
  • anonymous
=(1-cosθ^2)/(1+cosθ)
anonymous
  • anonymous
=(1-cosθ)(1+cosθ)/(1+cosθ) then we simplfy we know that a^2 - b^2=(a-b)(a+b) @Madgirlwithabluebox
anonymous
  • anonymous
so we get after simplifying the result =(1-cosθ) did u understand @Madgirlwithabluebox
Madgirlwithabluebox
  • Madgirlwithabluebox
Uh no? I get that since there was (1+cosθ)/(1+cosθ) you simplified and got the answer but i dont understand anything else
anonymous
  • anonymous
so? You understood it or no now ?
Madgirlwithabluebox
  • Madgirlwithabluebox
I think ,
freckles
  • freckles
does this make sense: assuming y not -1 simplifying (1-y^2)/(1+y) \[\frac{1-y^2}{1+y}=\frac{(1-y)(1+y)}{1+y}=\frac{\cancel{(1+y)}(1-y)}{\cancel{1+y}}=1-y\]

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