Trigonometry noob

[mufc802]

I'm trying to derive the factor formulae.

sinP + sinQ =2sin(P+Q/2)cos(P-Q/2) <<<< Prove this.

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So I know that sin(A+B)= sinAcosB + cosAsinB & Sin(A-B) = sinAcosB - cosAsinB.

so sin(A+B) + sin(A-B) = sinAcosB + cosAsinB + sinAcosB - cosAsinB
sin(A+B) + sin(A-B) = 2sinAcosB.

P=A+B ... Q=A-B

Now I don't get this part..
It says A=P+Q/2 and B=P-Q/2.. How do you get to that?

 

[RomanNose]

Silumataneous equation
Because
P+Q=2A
P-Q=2B

 

[mufc802]

Thanks.