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Verify, then find which is NOT equivalent : (Picture below)

Trigonometry
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1 Attachment
\[\frac{ cosx }{ sinx }\]
Can you show me how to figure that out?

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Other answers:

sure
sorry
\[\sin(\pi/2-x)\csc\]
is this the question
because in the picture the question does not seem right
if this is the question
\[\sin(\frac{ \pi }{2 }-x)=\sin(\frac{ \pi }{ 2 })cosx-\cos(\frac{ \pi }{ 2 })sinx=1.cosx-0.sinx=cosx\]
having this in mind, let us insert it in the original expression
\[\sin(\frac{ \pi }{2 }-x)cscx=cosxcscx=cosx.\frac{ 1 }{ sinx }\]
cosx/sinx=cotx=1/tanx
done
Thank you! I have another one that maybe you could help me with?
for sure
okay, hold on let me get it..
If you could do it all in one message that would be great so I can follow along easier.
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\[\frac{ cscA-sinA }{ \cot ^{2}A }=\frac{\frac{ 1 }{sinA }-sinA }{ \frac{ \cos ^{2}A }{ \sin ^{2}A } }=\frac{ \frac{ 1-\sin ^{2}A }{sinA } }{ \frac{ \cos ^{2}A }{\sin ^{2} A} }\] \[\frac{ 1-\sin ^{2}A }{sinA }.\frac{ \sin ^{2} A}{ \cos ^{2}A }=\frac{ \cos ^{2}A sinA}{ cosA }=sinAcosA=\frac{ 1 }{2 }\sin(2A)\]
Here is the final answer
So what's the final answer?
\[\frac{ 1 }{ 2 }\sin(2A)\]
does it make sense
uhmm.. yeah sort of. im terrible at this whole simplifying thing. up for a few more?
If you practice, it is not that hard my friend
i got all of the verifying ones but this one..
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I am going for launch. If you stay for 30 minutes i will get back to you.
I'll be here all evening. Thank you! Have a good time :)
\[\frac{ \cos \alpha-\cos \beta }{ \sin \alpha+\sin \beta }+\frac{ \sin \alpha-\sin \beta }{ \cos \alpha+\cos \beta}=\] \[\frac{ \cos ^{2}\alpha-\cos ^{2}\beta+\sin ^{2}\alpha-\sin^2\beta }{(\sin \alpha+\sin \beta)(\cos \alpha +\cos \beta)}\] =\[\frac{ \cos^2 \alpha+\sin^2\alpha-(\sin^2\beta +\cos^2\beta) }{(\sin \alpha+\sin \beta)(\cos \alpha+\cos \beta) }=\frac{ 1-1 }{(\sin \alpha+\sin \beta) (\cos \alpha+\cos \beta) }=0\]
it is verified
how is the denominator verified? nothing was done to it?
since it does not have any significance to simplify the denominator, we can leave it as it is.
How do you know if it has significance to simplify it or not?
In this particular problem, the purpose is to simplify the right hand side to zero. That tells us the numerator of the RHS has to be siplified to zero. our focus should be mostly on working out the numerator.
ohh okay. thanks.
it is my pleasure

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