SOLUTION: Sorry. Last one was screwed up. sinx/sinx+cosx = tanx/1+tanx

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Question 95717: Sorry. Last one was screwed up.

sinx/sinx+cosx = tanx/1+tanx

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
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sinx%2F%28sinx%2Bcosx%29+=+tanx%2F%281%2Btanx%29
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Use the identity:
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tanx+=+sinx%2Fcosx
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and on the right side substitute sinx%2Fcosx for tanx to get:
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sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2F%281%2B%28sinx%2Fcosx%29%29
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The denominator contains 1. Replace 1 with an equivalent cosx%2Fcosx to make the equation
become:
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sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2F%28%28cosx%2Fcosx%29%2B%28sinx%2Fcosx%29%29
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Notice now that the two terms in the denominator both have the common denominator
of cosx. Because they have the common denominator their numerators can be added over
that common denominator to get:
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sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2F%28%28cosx%2Bsinx%29%2Fcosx%29
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Note that on the right side you are dividing by the fraction %28%28cosx%2Bsinx%29%2Fcosx%29
To divide by a fraction you can invert the fraction and multiply. This converts the problem
to:
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sinx%2F%28sinx%2Bcosx%29+=+%28sinx%2Fcosx%29%2A%28%28cosx%29%2F%28cosx%2Bsinx%29%29
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On the right side cancel the cosx terms in the denominator and numerator:
.

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Notice that with this set of cancellations the right side now equals the left side of
the equation. Therefore, the original problem has been proven.
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Hope this helps you to understand trig a little better.
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