We have been working on proving identities and it's a subject I just can't get my brain around

We have been working on proving identities and it's a subject I just can't get my brain around. A few of the problems we've been given have made me stumble.

cotx/1+tan(-x) + tanx/1+cot(-x) = cotx + tanx +1

I figure on this one, with using identities, I can get:

cotx/1-tanx + tanx/1-cotx = cotx + tanx +1

But I can't get past there, and I don't even know if that's right.

The other problem is:

sinx + tanx/1 + secx = sinx

With using identities, I can get:

sinx + (sinx/cosx) / 1 + (1/cosx) = sinx