This was probably my favorite blog post. It helped me better understand trig verification and how to use trig identities to verify the trig function. In the first step I changed cos^2x-1 to -sin^2x because they equal each other. Then I changed tan^2x+1 to sec^2x because they also equal each other. I know this because of the trig identities. I also know that sec^2x=1/cos^2x so I changed that in the next step. Then I multiplied the -sin^2x by the 1/cos^2x to get -sin^2x/cos^2x and sin^2x/cos^2x=tan^2x and if you just add the negative you end up with -tan^2x.