Question

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

Answer 1

`(-cos^2x)/(1+sin^2x)`

Explanation:

Use the Pythagorean trigonometric identity, `color(blue)(sin^2x+cos^2x=1)`, to simplify "`sin^2x`" in the numerator.

`(sin^2x-1)/(1+sin^2x)`

`=((1-cos^2x)-1)/(1+sin^2x)`

`=color(green)(|bar(ul(color(white)(a/a)(-cos^2x)/(1+sin^2x)color(white)(a/a)|)))`