Please handwrite the answer, it would be appreciated!

d) If L' = -1212 A? _ 1 a 1 a sing On (Sine + sin-0 062' show that L? Y,m (12) = h21(1 + 1) Ym(1) where Y" (0) = 21 + 1 (1 - [ml!) 4TT (1 + Im! !) p/ml (cose ) cimob and Per (ac) satisfy differential equations for the associated Legendre polynomials. e) Show LY,m(1) = hmY,m(1). f) Defining Lt = La tiLy, show LL_ = 12 - 13 + hL. g) Show L+ |l, m) = VI(1+1) - m(m +1) |l, m+1) h) Calculate (1, m| L2 |1, m) without doing an integral.