I have a couple problems I cannot solve, please help me!

1. tan(x)/sec(x) + cot(x)/csc(x) =sin(x)+cos(x)

2 (1-tan(x))^2 = sec^2(x) - 2tan(x)

3. sin(x)/csc(x)-1 + sin(x)/csc(x)+1 = 2tan^2(x)

4. sin(x)[sec(x)-csc(x)] = tan(x)-1

Most of these types of things can be solved if you remember these definitions and identifies:

(1)

(2)

(3)

(4)

(5)

In addition to those, you sometimes need to look up double-angle formulas and a few similar things.

I'll do #1. You try the others.



substituting from #2, #3, #4, and #5:





qed