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Question Number 29837 by abdo imad last updated on 12/Feb/18

l e t g i v e T_{n} (x) = c o s (n a r c o s x) w i t h x \in [- 1, 1]

1) p r o v e t h a t T_{n} i s a p o l y n o m i a l a n d T_{n} \in Z [x]

2) c a l c u l a t e T_{1}, T_{2}, T_{3}, a n d T_{4}

3) p r o v e t h a t T_{n + 2} (x) = 2 x T_{n + 1} (x) - T_{n} (x)

4) f i n d t h e r o o t s o f T_{n} a n d f a c t o r i z e T_{n} (x) .