How do you simplify (sin^2x-1)/(1+sin^2x)?

Mar 31, 2016

$\frac{- {\cos}^{2} x}{1 + {\sin}^{2} x}$

Explanation:

Use the Pythagorean trigonometric identity, $\textcolor{b l u e}{{\sin}^{2} x + {\cos}^{2} x = 1}$, to simplify "${\sin}^{2} x$" in the numerator.

$\frac{{\sin}^{2} x - 1}{1 + {\sin}^{2} x}$

$= \frac{\left(1 - {\cos}^{2} x\right) - 1}{1 + {\sin}^{2} x}$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \frac{- {\cos}^{2} x}{1 + {\sin}^{2} x} \textcolor{w h i t e}{\frac{a}{a}} |}}}$