# I need to prove trigonometric equation \tan 2x=\frac{2 \sin x \cdot

I need to prove trigonometric equation
$\mathrm{tan}2x=\frac{2\mathrm{sin}x\cdot \mathrm{cos}x}{{\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x}$
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esfloravaou
Hints:
$\mathrm{cos}2x-\mathrm{sin}2x=\mathrm{cos}2x$
$2\mathrm{sin}x\mathrm{cos}x=\mathrm{sin}2x$
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Orlando Paz
Note that
$\mathrm{sin}\left(2x\right)=2\mathrm{sin}x\mathrm{cos}x$
$\mathrm{cos}2x={\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x$
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nick1337

If you know $\mathrm{sin}2x=2\mathrm{sin}x\mathrm{cos}x$ and $\mathrm{cos}2x={\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x$
Then $\mathrm{tan}2x=\frac{\mathrm{sin}2x}{\mathrm{cos}2x}$