trigonometric identities and there applications

In the image provided can someone explain why P+Q and P-Q becomes divided by 2 on the RHS of the equation.

What makes it become over 2 and why?

Many thanks

S

In the image provided can someone explain why P+Q and P-Q becomes divided by 2 on the RHS of the equation.

What makes it become over 2 and why?

Many thanks

S

It would have helped if you told us which part of the working you don't understand. It could be this part:


$\displaystyle A+B=P$
$\displaystyle A-B=Q$

Adding the equations together

$\displaystyle 2A=P+Q \Rightarrow A=\frac{P+Q}{2}$

Or subtracting the equations

$\displaystyle 2B=P-Q \Rightarrow B=\frac{P-Q}{2}$


If this doesn't help then please explain which parts of the working you understand and which you don't.