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!! :)

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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
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does it help to know that \[\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}\]?
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
so for the first one \[\cos(\theta)\tan(\theta)=\cos(\theta)\frac{\sin(\theta)}{\cos(\theta)}=\sin(\theta)\]

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Other answers:

it is mostly algebra the cosines cancel
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.
the second one is completely different it is derived from the "subtraction angle" formula \[\sin(\alpha-\beta)=\sin(\alpha)\cos(\beta)-\cos(\alpha)\sin(\beta)\]
put \(\alpha=\frac{\pi}{2}\) and \(\beta=\theta\) and you get it
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?
Sorry for the weirdness, I'm not super sure how to use the equation button. I meant: \[\cos (\theta)\]
yes the first one is B
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.
You have it correct.
Thanks both of you! :3
you're welcome

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