OK, after help from here, I tried 4 more questions and thought i got the hang of this. Now i have another dilemma. :S

By expressing: tan(alpha + beta) = sin(alpha + beta)/cos(alpha + beta)

Prove that: tan(alpha + beta) = tan alpha + tan beta/1 - tan alpha tan beta

Here are my first steps:

= sin(alpha + beta)/cos(alpha + beta)

= sin alpha cos beta + cos alpha sin beta/cos alpha cos beta - sin alpha sin beta

now im stuck,

should i cancel out the cos and sin from top and bottom?

i tried that, but that didn't work. after i thought, since i was lookin for tan in my answer, i wouldsin / cos = tan

that also did not work out.... (or maybe i did something wrong)

please guide me.