question in polar coordinates

i am going through a solution and there is a part i dont understand

it gives u = x+y
v = x-y

then it converts to polar
x=rcosT
y=rsin¿

so far so good

but then he derives

Vr = ucos¿ +vsinT
V¿ = -usin¿ +vcos¿

how did he get the vr and V¿ ?

any input would be appreciated.
c_hocklandAsked:
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TommySzalapskiConnect With a Mentor Commented:
I'm assuming T and ¿ are both supposed to be theta

x=rcosT
y=rsinT

(1)        u = x+y so u = rcosT + rsinT
(2)        v = x-y so v = rcosT - rsinT

Now work it backwards

vr = ucosT +vsinT
So
(rcosT - rsinT)*r = (rcosT + rsinT)cosT + (rcosT - rsinT)sinT

Now simplify that and remember your trig identities (cos^2(x) + sin^2(x) = 1, etc) and you should eventually get down to something like 1=1. This will prove it.
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c_hocklandAuthor Commented:
thank u sir!
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