# How do you simplify 2tanxcos^2x?

Nov 20, 2015

$2 \tan \left(x\right) {\cos}^{2} \left(x\right) = \sin \left(2 x\right)$

#### Explanation:

$\tan \left(x\right) = \sin \frac{x}{\cos} \left(x\right)$

So
$\textcolor{w h i t e}{\text{XXX}} 2 \tan \left(x\right) {\cos}^{2} \left(x\right)$

$\textcolor{w h i t e}{\text{XXX}} = 2 \sin \frac{x}{\cancel{\cos \left(x\right)}} \cdot \cancel{\cos \left(x\right)} \cdot \cos \left(x\right)$

$\textcolor{w h i t e}{\text{XXX}} = 2 \sin \left(x\right) \cos \left(x\right)$

which by the Double Angle Formula for Sines
$\textcolor{w h i t e}{\text{XXX}} = \sin \left(2 x\right)$
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