(sin

^{2}θ-cos

^{2}θ)/(1-tan

^{2}θ)=-cos

^{2}θ

So, the above is the equation that I have to verify.

I think the first step to this equation is

-1 (sin^{2}θ-cos^{2}θ)/(1-tan^{2}θ)=-cos^{2}θ

This is incorrect. You have only multiplied the left hand side by -1.
-1 (-(1))/(-1(sec

^{2}θ)=-cos

^{2}θ <-- So... I hope you can kinda get my train of thought here, but I feel like it's completely wrong (

)

You have been given $\displaystyle (sin^{2}\theta-cos^{2}\theta)/(1-tan^{2}\theta)=-cos^{2}\theta$ If you want to multiply by -1 you have to multiply both the left had side and the right hand side.

1/(-1(sec

^{2}θ) = -cos

^{2}θ

Then by simplifying the above you get -cos

^{2}θ ~ however... the blackboard answer I get to select from... doesn't even have an answer close to what I did above...

Please help