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Showing posts with label Chebyshev polynomial. Show all posts
Showing posts with label Chebyshev polynomial. Show all posts

Mathematical induction III


Today, we will solve some more problems using mathematical induction.


Problem 7. Observe that $$\cos 2 \alpha = 2 \cos^2 \alpha - 1$$
Prove that we can write $\cos n\alpha$ as a polynomial of $\cos \alpha$.