Question

How do you simplify `sinx/(1 + sinx) - sinx/(1 -sinx)`?

Answer 1

You should get `-2tan^2x` as a final answer.

Explanation:

`(sinx)/(1 + sinx) - sinx/(1 - sinx)`

`=(sinx(1 - sinx) - sinx(1 + sinx))/((1 + sinx)(1 - sinx)`

`=(sinx - sin^2x - sinx - sin^2x)/(1 - sin^2x)`

Using the pythagorean identity `cos^2x + sin^2x = 1`

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

Using the quotient identity `tanx = sinx/cosx`

`=-2tan^2x`

Hopefully this helps!