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?

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

I know it reduces to tanx, but how would I show the work for a problem like this?

Thanks so much for any help!