1. In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

Show that

$\frac{\text{sin}(A+B)+\text{sin}(A-B)}{\text{cos}(A+B)+\text{cos}(A-B)}\equiv\text{tan}AA,B\neq(k+\frac{1}{2}) \pi$