Passo 1
$bar(CP)^2=bar(AC)^2+bar(AP)^2-2*bar(AC)*bar(AP)*cosx rarr$
$rarr bar(CP)^2=1+4sin^2x-4cosxsinx$
Passo 2
$[sin^2x=1/2-1/2cos2x] ^^ [cosxsinx=1/2sin2x] rarr$
$rarr bar(CP)^2=3-2cos2x-2sin2x rarr$
$rarr bar(CP)^2=3-2sqrt2(sqrt2/2cos2x-sqrt2/2sin2x) rarr$
$rarr bar(CP)^2=3+2sqrt2sin(2x-\pi/4)$
Passo 3
$[0 lt= x lt= \pi/2] rarr [0 lt= 2x lt= \pi] rarr [-\pi/4 lt= 2x-\pi/4 lt= 3/4\pi]$
Poichè:
$-\pi/4 lt= \pi/2 lt= 3/4\pi$
il massimo si ha quando:
$[2x-\pi/4=\pi/2] ^^ [sin(2x-\pi/4)=1] rarr [x=3/8\pi]$