itsonlycdeee
  • itsonlycdeee
Prove the identity. sec θ − cos(−θ) = sin^2θ/cosθ I'm trying to transform the left side to the right side & so far I got: 1/ cosθ - cos(-θ) = 1/cosθ - cosθ =
Mathematics
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chestercat
  • chestercat
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cwrw238
  • cwrw238
sin^2θ/cosθ = (1 - cos^2θ)/cosθ = 1 / cosθ - cos θ = secθ - cos θ
hartnn
  • hartnn
if you want to continue from where you have left, try to make a common denominator \(\dfrac{1}{\cos \theta}- \cos \theta \times \dfrac{\cos \theta}{\cos \theta}=\dfrac{1-\cos^2 \theta}{\cos \theta}\) and lastly the use of \(\sin^2 x+\cos^2 x=1\) will lead you to right side :)
itsonlycdeee
  • itsonlycdeee
@hartnm okay, that's what I'm attempting right now.

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hartnn
  • hartnn
good, did you get what i did ? if yes, can you continue ?
itsonlycdeee
  • itsonlycdeee
Yes, it becomes sin^2θ/ cosθ. Thank you so much!
hartnn
  • hartnn
you're most welcome ^_^
cwrw238
  • cwrw238
with these problems its often easier to start with the more complicated side as i did here
itsonlycdeee
  • itsonlycdeee
@cwrw238 yeah, it'd take a few steps longer to go from the simpler side to the difficult one.

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