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I dont understand why sin(1+2n)(pi/2)=(-1)^n and sin(2n-1)(pi/2)=(-1)^n+1. Can you please explain it to me. Thank you

I dont understand why sin(1+2n)(pi/2)=(-1)^n and sin(2n-1)(pi/2)=(-1)^n+1. Can you please explain it to me. Thank you

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 19E
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I dont understand why sin(1+2n)(pi/2)=(-1)^n and sin(2n-1)(pi/2)=(-1)^n+1. Can you please explain it to me. Thank you

G Gmail b In Problems 11-24 expand the gi x A bartleby.com/solution-answer/chapter-113-problem-24e-differential-equations-with-boundary-value-problems-mindtap-course-list-9th-edition/9781337604918/in-problems-1124-expand-the-given-function-in-an-appropriate-cosine-or-sine-s. ☆ B Paused = bartleby Q Search for textbooks, step-by-step explanations to homework questions, ... E Ask an Expert e Bundle: Differential Equations with Bou... < Chapter 11.3, Problem 24E > Substitute the value of f (x) as cos x in the above equation. 2 an = cos x cos -x dx */2 cos x cos 2nx dx пл 2 cos x cos -x dx */2 Further solve the above equation. a, = 4 cos (1+ 2n) x dx + cos (2n – 1)x dr sin (1+2n)x | % (1+2n) sin (2n-1)x + lo (2n-1) sin ( (1+2n)(들)) + (1+2n) sin ((2n-1)()) (2n-1) For any non-negative value of n the value of the term sin ( (1 + 2n) ()) is always 1 and the value of the term sin (1 – 2n) (5)) is 1 for even values of n and –1 for odd values of n. Further solve the above equation. ao (-1)" (1+2n) (-1)*+1 (2n-1) Privacy - Terms (n ie oven) image (39).png Show all
Transcribed Image Text:G Gmail b In Problems 11-24 expand the gi x A bartleby.com/solution-answer/chapter-113-problem-24e-differential-equations-with-boundary-value-problems-mindtap-course-list-9th-edition/9781337604918/in-problems-1124-expand-the-given-function-in-an-appropriate-cosine-or-sine-s. ☆ B Paused = bartleby Q Search for textbooks, step-by-step explanations to homework questions, ... E Ask an Expert e Bundle: Differential Equations with Bou... < Chapter 11.3, Problem 24E > Substitute the value of f (x) as cos x in the above equation. 2 an = cos x cos -x dx */2 cos x cos 2nx dx пл 2 cos x cos -x dx */2 Further solve the above equation. a, = 4 cos (1+ 2n) x dx + cos (2n – 1)x dr sin (1+2n)x | % (1+2n) sin (2n-1)x + lo (2n-1) sin ( (1+2n)(들)) + (1+2n) sin ((2n-1)()) (2n-1) For any non-negative value of n the value of the term sin ( (1 + 2n) ()) is always 1 and the value of the term sin (1 – 2n) (5)) is 1 for even values of n and –1 for odd values of n. Further solve the above equation. ao (-1)" (1+2n) (-1)*+1 (2n-1) Privacy - Terms (n ie oven) image (39).png Show all
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