# How to factor and simplify the expression 4tan^2x-4tan^2xsin^2x using fundamental identities?

Oct 29, 2017

$4 {\sin}^{2} x$

#### Explanation:

$4 {\tan}^{2} x - 4 {\tan}^{2} x {\sin}^{2} x$

Hmmm. well, you can factor out $4 {\tan}^{2} x$, giving:

$4 {\tan}^{2} x \left(1 - {\sin}^{2} x\right)$

...since ${\sin}^{2} x + {\cos}^{2} x = 1$, then $1 - {\sin}^{2} x = {\cos}^{2} x$

So you can rewrite the expression as:

$4 {\tan}^{2} x {\cos}^{2} x$

...then, you can rewrite ${\tan}^{2} x$ as ${\sin}^{2} \frac{x}{\cos} ^ 2 x$, so this makes your expression:

$4 {\sin}^{2} \frac{x}{\cos} ^ 2 x \cdot {\cos}^{2} x$

...and the 2 ${\cos}^{2} x$ terms cancel, leaving:

$4 {\sin}^{2} x$

...which I think may be the best you can do.

GOOD LUCK