I'm getting very confused...there are too many formula for this!

Prove:

1. sin (A+B) + cos (A-B) $\displaystyle \equiv$ (sin A+ cos A)(sin B + cos B)

2. tan (A+B) - tan A $\displaystyle \equiv \frac{sin B}{cos A cos (A+B)}$

And one more extra:

3. In triangle ABC, AB=p, BC=3p, and $\displaystyle \angle ABC=60^o$. The bisector of the angle ABC meets AC at the point T. Find AT and CT in terms of p.

Answer: $\displaystyle AT=\frac{p}{4}\sqrt{7}; CT=\frac{3p}{4}\sqrt{7}$