Question: 7. Let a: be a. real number. We let no = 1, u1 = c033: and dene (an) in such a way that for all

7. Let a: be a. real number. We let no = 1, u1 = c033: and dene (an) in such a way that for all n 2 0, an\" = 2u1un+1 an. Show that for all n 2 0 we have an = cos(n:1:). Note: In the induction step, you can use the trigonometric formulas cos(a + b) = cos aces b sin a Sin?) and cos(a. b) = cos acosb + sin a sin b

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