Step 1: Expand the tan^2x to sin^2x / cos^2x Step 2: Expand the 1 to cos^2x / cos^2x. This can be done because cos^2x / cos^2x = 1 for all real numbers, or fake numbers, who knows? Step 3: Group the bottom sin^2x / cos^2x and cos^2x / cos^2x to make it into (sin^2x + cos^2x) / cos^2x. Step 4:Change(sin^2x + cos^2x) to 1 because (sin^2x + cos^2x) = 1 with the Pythagorean identity. Step 5: Cancel out the top cos^2x with the bottom cos^2x to leave just sin^2x.
From this project, I learned valuable skills on working through a trig identity. I learned all of the basic identities in greater depth. This also helped me learn how to work through this kind of identity and do it again in the future.