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Problem with Trig Identity

Posted on 2014-11-17
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Last Modified: 2014-11-17
Hi,

I can't seem to prove the following trig identity, or where to start. Any ideas?

Thanks!
TrigIdentity.jpg
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Question by:Computer Guy
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by:d-glitch
ID: 40447347
Start by replacing tan and cot with their sin and cos equivalents.  
This should be  a four line proof.
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by:Computer Guy
ID: 40447484
So  1+sin/cos would = cos * sin/cos
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by:d-glitch
ID: 40447519
>>  So  1+sin/cos would = cos * sin/cos

That is not true, nor one of the steps.

You have to methodically transform the Left-Hand-Side of the equation until it matches the right.

Half of the first step is to replace   1 + tan    with    1 + sin/cos
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by:Computer Guy
ID: 40447542
Woops, that part I knew.

I mean to say that

(cos/1)/(1+(sin/cos)) where the 1's and the cos cancel out left with sinx for the first part, right?
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by:d-glitch
ID: 40447573
After the first step, you will still have two terms on the LHS

One of them will be     cos / (1 + sin/cos)       The other will be similar.
But there is nothing to cancel out yet.
The two terms have to simplified [ Step 2]
Then combined [ Step 3]
At this point, you will be able to factor and cancel [ Step 4]
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by:Computer Guy
ID: 40447620
Not sure how to simplify them.
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by:d-glitch
ID: 40447754
The problem with this term   cos / (1 + sin/cos)   is that there is a fraction in the denominator.
How do you simplify that?    

If the term were   3 / (1 + 2/7)  what would you do?
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by:d-glitch
ID: 40448005
I don't imagine that this identity is particularly useful, but it is quite simple.

The only trig you need to know is that   tan = sin/cos   and   cot = cos/sin
The rest is simple algebra.

The way to solve this is to assume that it is solvable and plug away.  It is really a 60 second problem.
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by:Computer Guy
ID: 40448176
I know what tan and cot equal. I just don't know what to do with the (1+sin/cos)
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d-glitch earned 500 total points
ID: 40448250
After substituting for   tan  

The first term becomes   cos / (1 + sin/cos)  

To simplify this you have to eliminate the fraction in the denominator (bottom).
You can multiply this term by   cos / cos   to get   cos² / (cos + sin)
You have to do something similar to the second term.
That will complete [ Step 2]
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