please solve these mathematical question

[Syed Wasif Mobin]

sorry for the earlier mail. i have changed the character thier names..

Q1. Show that
u(r,theta) = Brn  Sin n*theta .
Satisfy the laplace equation in polar coordinate.

u rr +1/r u r + 1/r2 u thetatheta  = 0

Q2. A circular plate given by 0 <= r <= 1, pi <= theta <= pi kept at 50 Centigrade and a portion r =1 , -pi <= theta <= 0 kept at &#8211; 50 Centigrade, show that the steady state temp u (in centigrade) at (r,theta) is given by u (r,theta) = &#931; Bnrn sin ntheta  ,  n= 1 to infinity
         Where Bn ={0    (even)
                  {200/n*pi  (odd)

[Hassan Aurag]

Is it hard to prove or disprove Question 1?

It seems to me it is straightforward