I'm trying to verify these trigonometric identities.

Question

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

2. csc(x) - sin(x) = cos(x) * cot(x)

3. 1/tan(x) + 1/cot(x) = tan(x) + cot(x)

4. csc(-x)/sec(-x) = -cot(x)

Answer 1

Can you post your attempts?
I will give you a kickstart:
1/(sec(x)tan(x))
=1/(1/cos(x) * sin(x)/cos(x))
=cos²(x)/sin(x)
=(1-sin²(x))/sin(x)
=csc(x) - sin(x)