prove equation equals $-1$ I was wondering if it was possible to prove that
$\left( \frac{( a^2 - c^2 + (\frac{d}{c}a)^2-d^2)}{ \sqrt{(a-c)^2+(\frac{d}{c}a)-d)^2} \sqrt{(a+c)^2+(\frac{d}{c}a)+d)^2}} \right) = -1$ when $a,d,c \in [-1,1]$ and $|a|<c$, and $|b|<d$? 
Attempt: By Asdrul, I know that
$$\left[(a-c)^{2}+\bigg(\frac{d}{c}a-d\bigg)^{2}\right]\cdot\left[(a+c)^{2}+\bigg(\frac{d}{c}a+d\bigg)^{2}\right]=\frac{1}{c^4}( c^{2}+d^{2}) ^{2}\left( a^2-c^2\right) ^{2}$$
So applying this, I have that the above equals
$\frac{c^2(a^2-c^2+(\frac{da}{c})^2-d^2)}{(c^2+d^2)|a^2-c^2|}$

Hint: note that
$$\left[(a-c)^{2}+\bigg(\frac{d}{c}a-d\bigg)^{2}\right]\cdot\left[(a+c)^{2}+\bigg(\frac{d}{c}a+d\bigg)^{2}\right]=\frac{1}{c^4}( c^{2}+d^{2}) ^{2}\left( a^2-c^2\right) ^{2}$$
