anonymous
  • anonymous
I'm really struggling with establishing identities and I would seriously love some help. Here are two questions I need answered: https://i.imgur.com/BnFBQ33.png and https://i.imgur.com/nK2VeCH.png I'm not sure where to start with either of these, and I really would like to know how to solve them and what the answers are. Any advice would be helpful! Thanks in advance!! :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
does it help to know that \[\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}\]?
anonymous
  • anonymous
Yes! I found a sheet of a few things like that but I'm not exactly sure how they work. http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
anonymous
  • anonymous
so for the first one \[\cos(\theta)\tan(\theta)=\cos(\theta)\frac{\sin(\theta)}{\cos(\theta)}=\sin(\theta)\]

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anonymous
  • anonymous
it is mostly algebra the cosines cancel
jim_thompson5910
  • jim_thompson5910
They have the answer choices written out in one long line, which makes it a bit tricky to sort things out. I find it better to have it written out like this \[\Large \cos(\theta)\tan(\theta) = \sin(\theta)\] \[\Large \cos(\theta){\color{red}{\tan(\theta)}} = \sin(\theta)\] \[\Large \cos(\theta){\color{red}{\frac{\sin(\theta)}{\cos(\theta)}}} = \sin(\theta)\] At this point, I'm sure you see what cancels. Throughout the whole process, the right side stays the same.
anonymous
  • anonymous
the second one is completely different it is derived from the "subtraction angle" formula \[\sin(\alpha-\beta)=\sin(\alpha)\cos(\beta)-\cos(\alpha)\sin(\beta)\]
anonymous
  • anonymous
put \(\alpha=\frac{\pi}{2}\) and \(\beta=\theta\) and you get it
anonymous
  • anonymous
Okay, I think I get the canceling thing. One the first one at least. for the first question would the answer would be B since the \[\cos()\] cancel out and \[\tan( \theta)\] equals sin over cos, which equals the others. Is this correct?
anonymous
  • anonymous
Sorry for the weirdness, I'm not super sure how to use the equation button. I meant: \[\cos (\theta)\]
jim_thompson5910
  • jim_thompson5910
yes the first one is B
anonymous
  • anonymous
I'm still a little stuck with the second question. Would it be C since the subtraction angle formula comes out to be sin(π/2−θ)=sin(π2)cos(θ)−cos(π/2)sin(θ) which matches the first part of the equation? Some of this stuff is going over my head.
jim_thompson5910
  • jim_thompson5910
You have it correct.
anonymous
  • anonymous
Thanks both of you! :3
jim_thompson5910
  • jim_thompson5910
you're welcome

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