Math Help - prove- trigo

1. prove- trigo

cosA+sinA= sec2A + tan2A
cosA-sinA

cotA+tanA=sec2A
cotA-tanA

HOW o???

2. For the first one, multiply by $\frac{\cos{A}+\sin{A}}{\cos{A}+\sin{A}}$

You will need the following identities:
$\sin^2{A} + \cos^2{A} = 1$

$\cos^2{A} - \sin^2{A} = \cos{2A}$

For number 2, recall that
$\tan{A} = \frac{\sin{A}}{\cos{A}}$

$\cot{A} = \frac{\cos{A}}{\sin{A}}$

Replace and combine fractions, then simplify.

3. For first one , how about tan2A?
THX!