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

Solutions relying entirely on calculator technology are not acceptable.

By writing $(X+Y-Z)$ as $((X+Y)-Z)$ and using the identities for $\text{sin}(A\pmB)$ and $\text{cos}(A\pmB)$, show that

$\text{sin}(X+Y-Z)\equiv\text{sin}X\text{cos}Y\text{cos}Z+\text{cos}X\text{sin}Y\text{cos}Z-\text{cos}X\text{cos}Y\text{sin}Z+\text{sin}X\text{sin}Y\text{sin}Z$