Help Deriving Fresnel's Equations Please

[Fjolvar]

I'm trying to derive/simplify Fresnel's equation for r perp from its form:

[n_i cos $$\theta$$_i - n_t cos$$\theta$$ _t] / [n_i cos $$\theta$$ _i + n_tcos$$\theta$$_t]

to ---> - sin ($$\theta$$_i - $$\theta$$_t) / sin ($$\theta$$_i + $$\theta$$_t)

From what I've gathered you need to use Snell's law n_tsin$$\theta$$_t = n_isin$$\theta$$_i

and also substitute the identity cos^2$$\theta$$ = $$\sqrt{1-sin^2\theta}$$

I've been playing with the substitutions along with the trig identity Sin (a-b) = sinacosb - cosasinb... but i cannot get it to work. Any help would be greatly appreciated. I'm stuck mostly on getting rid of the square root after making the substitution to get the trig identity form. Thanks.

 

[Fjolvar]

Even a hint will be appreciated if you don't want to show the derivation.