I need help verifying these trig identites:

cos(x)/(1-sin(x))=sec(x)+tan(x)

1+cos(x)=sin(x)=2csc(x)

sin(x)+cos(x)/sin(x)-cos(x)-sin(x)/cos(x)=sec(x)*csc(x)

1. \frac{cos(x)}{1-sin(x)} = sec(x) + tan(x)

I think the easiest way to solve this is to rationalise the denominator of the left hand side.

\frac{cos(x)}{1-sin(x)} \times \frac{1+ sin(x)}{1 +sin(x)}= \frac{cos(x) + cos(x)sin(x)}{cos^2(x)}

You can continue now.

The second problem is not an identity. Can you repost it?

For the last problem, can you use more brackets? It'll help use understand the problem better.