I am trying to prove that $$ \frac {\sin (n+1) \theta}{\sin \theta}=\sum \limits _{l=0}^{n} P_l(\cos \theta)P_{n-l}(\cos \theta)$$. I found this identity on wikipedia but I am unable to prove it. If anyone has any hints it would be great.
2026-03-26 19:02:49.1774551769
Proving that $ \frac {\sin (n+1) \theta}{\sin \theta}=\sum \limits _{l=0}^{n} P_l(\cos \theta)P_{n-l}(\cos \theta)$
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