Im trying to study for my math 109/110 course in college

and trig. id's are giving me the hardest problems

we've learned about the identities for sin, cos, tan and excluding cot csc sec

Prove the identity

$\displaystyle tan x =\frac{sin 2x}{1+ cos 2x} $

also how is this and identity the x values are not the same at all I thought that what trig. identity means for every x value both have the same output

Also

how is

$\displaystyle \frac{cos^2t-sin^2t}{cos^2t} = 1- \frac{sin^2t}{cos^2t}$