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By replacing a with 2x in the Maclaurin series for sin x, we can see that (−1)n 2²n+1 x²n+1 (2n + 1)! sin(2x)= (a) Use the fact that sin²x = Note that cos x = Σ n=0 = In this question, you will find another path towards determining the Maclaurin series for sin(2x). n=0 1 - cos(2x) 2 (−1)”,2n (2n)! to obtain the Maclaurin series for sin² x.

By replacing a with 2x in the Maclaurin series for sin x, we can see that (−1)n 2²n+1 x²n+1 (2n + 1)! sin(2x)= (a) Use the fact that sin²x = Note that cos x = Σ n=0 = In this question, you will find another path towards determining the Maclaurin series for sin(2x). n=0 1 - cos(2x) 2 (−1)”,2n (2n)! to obtain the Maclaurin series for sin² x.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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By replacing a with 2x in the Maclaurin series for sin x, we can see that (−1)n 2²n+1 x²n+1 (2n + 1)! In this question, you will find another path towards determining the Maclaurin series for sin(2x). (a) Use the fact that sin² X = Note that cos x = ∞ n=0 (b) Use the fact that series for sin(2x). sin(2x) = Σ n=0 d dx 1 cos(2x) 2 (−1)¹x²n (2n)! -sin² x = to obtain the Maclaurin series for sin² x. 2 sin x cos x = sin(2x) to obtain the Maclaurin
Transcribed Image Text:By replacing a with 2x in the Maclaurin series for sin x, we can see that (−1)n 2²n+1 x²n+1 (2n + 1)! In this question, you will find another path towards determining the Maclaurin series for sin(2x). (a) Use the fact that sin² X = Note that cos x = ∞ n=0 (b) Use the fact that series for sin(2x). sin(2x) = Σ n=0 d dx 1 cos(2x) 2 (−1)¹x²n (2n)! -sin² x = to obtain the Maclaurin series for sin² x. 2 sin x cos x = sin(2x) to obtain the Maclaurin
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