Using the fundemental identities and the Pythagorean Identities, I go over multiple examples of verifying trigonometric identities.

It is very important in proofs that you do not handle it like an equation moving terms and factors from side to side.

I was corrected that what I am trying to prove should not be within the body of the proof. This implies it has already been assumed to be true. So proofs should be shown like this example:
cos^2(x)(tan^2(x)+1)=1
Proof:
cos^2(x)(tan^2(x)+1)=cos^2(x)*sec^2(x)
=cos^2(x)(1/cos^2(x))
=1