Verifying Trig Identities?

Hello there.

I am having some trouble in studying verifying trig identities for my Math final.

____1____ + _____1____ = 2Sec^2x

1-Sinx 1+Sinx

It's 1 over 1-Sinx plus 1 over 1 plus Sinx, equals 2 Sec squared x. I can't figure this one out. I think you have to get a common denominator, but I'm not sure, what to do after that.

1-Sinx

_________ = Sec^2x - 2secxtanx+tan^2x

1+Sinx

For this one, you work almost exclusively on the right side, no? I got (Secx-tanx)(Secx-tanx).

From there don't you use reciprocal identities? After that, I am stuck.

Any help would be appreciated. Also, since I am positive these will be on my final, can anyone give me general help/tips on solving these? A link to a good site would be very helpful. Thanks in advance.