Verifying Trigonometric Identities

Good day Math Help Forum Team!

I am quite confused about verifying identities, especially on complex numbers. I have insufficient examples on my book, therefore confusion is the result. I go several expressions which I think will help me, but I can't solve it.

1. 1/Tanx+Cotx = SinxCosx

2. Cosx/1+Sinx + Cosx/1-Sinx = 2Sec

3. Secx+1/Tanx = Tanx/Secx-1

4. Tan^2x/Sec^x + Sinx/1-Cosx = Cotx + Secx + Cscx

5. Tan^3x + SinxSecx-SinxCosx/Secx-cosx = TanxSecx+Sinx

Thank you very much Math Help Forum! More power!