Answer
See explanations below.
Work Step by Step
Step 1. List all the formulas of the Law of Cosines: $c^2=a^2+b^2-2ab\cdot cosC$, $b^2=a^2+c^2-2ac\cdot cosB$, $a^2=c^2+b^2-2bc\cdot cosA$
Step 2. Add the first two formulas to get $c^2+b^2=2a^2+b^2+c^2-2ab\cdot cosC-2ac\cdot cosB$ which leads to
$2a^2=2ab\cdot cosC+2ac\cdot cosC$, since $a\ne0$ we have $a=b\cdot cosC+c\cdot cosC$
Step 3. Repeat Step 2 for the other two Projection Laws by adding $a^2+b^2$ and $c^2+a^2$
