Verify the identity: (1-tan^2t)/(1+tan^2t)=2cos^2 t-1

As usual, start by replacing the tangent functions with its sine and cosine equivalent, an then simplify the resulting fraction. Look for the opportunity to apply some well-known identities which you should have memorized, such as sin^2t + cos^2t = 1, and the identites for cos(2t) and sin(2t).