Polar complex question, similtaneous equations

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Homework Statement


x=r*cos(theta) y=r*sin(theta)
Ur=Ux*cos(theta)+Uy*sin(theta)
Utheta=-Ux*r*sin(theta)+Uy*r*cos(theta)
Vr=Vx*cos(theta)+Vy*sin(theta)
Vtheta=Vy*r*sin(theta)+Vx*r*cos(theta)

cauchy rieman equations, Ux=Vy Uy=-Vx and for polar Ur=(Vtheta)1/r Vr=(Utheta)(-1/r)

show that Ux=Ur*cos(theta)-1/r*Utheta*sin(theta) and Vx=Vr*cos(theta)-1/r*Vtheta*sin(theta)

The Attempt at a Solution


I got told i need to use simultaneous equations.. I've tried soo amny times but all i get is Ux=Ux 0=0 or 1=1... please can someone put me on the right track
 
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ok i can work backwards form the answer, and see that is is correct... but i don't know how to show Ux and Vx from what i have got.
 
anyone?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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