Prove Trig Identities

speeddown

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Feb 20, 2015
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I've tried searching around and haven't been able to find anything on this one in particular. I've been working on it for about an hour now:



___2___ = sin2x
cotx + tanx


I haven't had much trouble with proving identities till now.
 
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Here's where I get stuck

=2cos(x)sin(x)+sin(x)cos(x)\displaystyle =\dfrac{2}{\dfrac{\cos \left(x\right)}{\sin \left(x\right)}\,+\,\dfrac{\sin \left(x\right)}{\cos \left(x\right)}}

I can get there, easy

But I'm not sure how they get the following:

=2cos(x)sin(x)cos2(x)+sin2(x)\displaystyle =\dfrac{2\cos \left(x\right)\sin \left(x\right)}{\cos ^2\left(x\right)\,+\,\sin ^2\left(x\right)}
 
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Don't forget what you learned about dividing by a fraction!

What did you get when you converted the terms in the denominator of the first line above to a common denominator, combined into one fraction, and then flipped and multiplied? ;)
 

Without using calculator - can you calculate (and express the sum as a fraction):

234+57 = ??\displaystyle \dfrac{2}{\dfrac{3}{4}\,+\,\dfrac{5}{7}} \ = \ ??
 
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