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  • 1 Post By bigyan1einstein
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April 18th, 2016, 07:20 PM   #1
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a horrible looking trigonometric identity

I am really stuck in the identity below.


Using sums and differences, I can simplify the terms with

Next, putting these results in the expression on the left side gives

I don't know what to do now. Could someone please help me? Thank you very much.

Last edited by skipjack; April 18th, 2016 at 10:51 PM.
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April 18th, 2016, 07:36 PM   #2
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Go to the link ... Look at #1, (a) and (c)

Sum and Product of sine and cosine
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April 18th, 2016, 10:20 PM   #3
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=(-2.sin(A+B/2).sin(A-B/2))/((2cosB+A/2.sinB-A/2)) [This is the product form of sin and cos for differences of different angles]
upon cancelling terms by adjusting signs you get
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April 18th, 2016, 11:46 PM   #4
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More parentheses would be needed; it's clearer if formatted neatly.

$\displaystyle \frac{\cos A - \cos B}{\sin B - \sin A} = \frac{-2\sin{\small\dfrac{A+B}{2}} \sin{\small\dfrac{A-B}{2}}}{2\cos{\small\dfrac{B+A}{2}} \sin{\small\dfrac{B-A}{2}}} = \frac{\sin{\small\dfrac{A+B}{2}}} {\cos{\small\dfrac{A+B}{2}}} = \tan\frac{A+B}{2}$
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horrible, identity, trigonometric

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