...The first question I think I have the correct answer to but wanted to double check.

The problem says prove the following identity...

sec x + csc x = csc x + csc x tan x

(1/cosx + 1/sin)=

sinx/(sinxcosx) + cosx/(sinxcosx)

(1/sinx)*(sinxcosx)= cscxtanx=secx

Does this answer make sense? no

working from the right side ...

The second question I have I need to reduce this to a single term.

tan (x+y) - tan y

-----------------------

1+ tan (x+y) tan y

use this identity ...

let and