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7. Let x be a real number. We let uo way that for all n > 0, un+2 = 1, u1 = cos x and define (un) in suc %3D 2u1Un+1 - Un. Show that for all n > 0 we ha |

7. Let x be a real number. We let uo way that for all n > 0, un+2 = 1, u1 = cos x and define (un) in suc %3D 2u1Un+1 - Un. Show that for all n > 0 we ha |

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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7. Let x be a real number. We let uo way that for all n > 0, Un+2 = cos x and define (un) in such a 2u1 Un+1 – Un. Show that for all n > 0 we have 1, ui Un = cos(nx). Note: In the induction step, you can use the trigonometric formulas cos(a + b) : = cos a cos b – sin a sin b and cos(a – b) = cos a cos b + sin a sin b. |
Transcribed Image Text:7. Let x be a real number. We let uo way that for all n > 0, Un+2 = cos x and define (un) in such a 2u1 Un+1 – Un. Show that for all n > 0 we have 1, ui Un = cos(nx). Note: In the induction step, you can use the trigonometric formulas cos(a + b) : = cos a cos b – sin a sin b and cos(a – b) = cos a cos b + sin a sin b. |
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