## Trig Identity Proof help

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
oboetoke
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### Trig Identity Proof help

[(sin(3x) + cos(3x))/(cos(x)-sin(x))] = 1 + 2sin2x

i've been working on this for along time and still cannot prove it.

stapel_eliz
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[(sin(3x) + cos(3x))/(cos(x)-sin(x))] = 1 + 2sin2x

i've been working on this for along time and still cannot prove it.
Since you've been working on this for some time, you've got some work you can show. Please reply with that, so we can see where you are. (You might be nearly to the solution!)

Please start with your substitution on the left-hand side for the triple angles. You may have started with the sum identities and the double-angle identities, or perhaps you started right away with the triple-angle identities.

Then maybe you factored the $3\sin(\theta)\cos^2(\theta)\, -\, 3\sin^2(\theta)\cos(\theta)$ and the difference of cubes $\cos^3(\theta)\, -\, \sin^3(\theta)$. Then you cancelled with the denominator, and so forth.

Either way, please start with the substitution. Thank you!

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