cos(xy)=0 identity?

Phi

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Dec 5, 2012
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So I was doing an implicit differentiation and I check the solutions manual and find that they were able to take one more step than I could manage in which two cosine functions magically disappear.
cosine mystery.jpg

I tried to use the sum identities (imagining that xy could be restated as the sum of x number of y), but can't seem to get anywhere. Seems like I'm missing an identity in my limited trig book.
 
So I was doing an implicit differentiation and I check the solutions manual and find that they were able to take one more step than I could manage in which two cosine functions magically disappear.
View attachment 2494

I tried to use the sum identities (imagining that xy could be restated as the sum of x number of y), but can't seem to get anywhere. Seems like I'm missing an identity in my limited trig book.

You are not missing trig identity - you are missing simple algebra!!

Factor out 'y' from numerator and factor out 'x' from the denominator.

What do you get?
 
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