dont understand why integral(cosnpix)/p)(cosmpi/p)=2*integral(cosnpix/p)(cosmpix/p). Can you please explain it to me. Thank you

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I dont understand why integral(cosnpix)/p)(cosmpi/p)=2*integral(cosnpix/p)(cosmpix/p). Can you please explain it to me. Thank you

M Inbox (38,433) - seabhaskar1150 x
M Inbox - pchandr4@binghamton.e X
A Homework 1
b In Problems 7-12 show that the
+
A bartleby.com/solution-answer/chapter-111-problem-12e-differential-equations-with-boundary-value-problems-mindtap-course-list-9th-edition/9781337604918/in-problems-712-show-that-the-given-set-of-functions-is-orthogonal-on-the-indicated-in. *
= bartleby
Q Search for textbooks, step-by-step explanations to homework questions, .
E Ask an Expert
e Bundle: Differential Equations with Bou...
< Chapter 11.1, Problem 12E >
To show: The given functions are orthogonal and to find out the
Problem 9E
norm.
Problem 10E
Problem 11E
Answer to Problem 12E
Problem 12E
The norm of the given functions are 1 ||= V2p, cos x ||= VP
Problem 13E
sin x ||= VP
and
Explanation of Solution
Given: The given functions are
{1, cos x, sin ".} for n = 1,2...m = 1,2.. in the interval [-p, p].
Calculation:
плх
Consider
cos
Mxx dx where n + m
COS
плх
плх
тлх
cos mAx dx == 2
cos
dx
(1)
cos
COS
-P
Use the formula 2 cos A cos B = cos (A – B) + cos (A + B)
cos mx dx =
(п — т) лх .
cos
(п + m) лх
cos
cos
+
P
p
Now, integrate the right hand side of above equation.
(n+m)
(n-m)x
sin
плх
cos MAX dx =
sin
2(n+m)x
Cos
2(n-m)x
Privacy · Terms
Transcribed Image Text:M Inbox (38,433) - seabhaskar1150 x M Inbox - pchandr4@binghamton.e X A Homework 1 b In Problems 7-12 show that the + A bartleby.com/solution-answer/chapter-111-problem-12e-differential-equations-with-boundary-value-problems-mindtap-course-list-9th-edition/9781337604918/in-problems-712-show-that-the-given-set-of-functions-is-orthogonal-on-the-indicated-in. * = bartleby Q Search for textbooks, step-by-step explanations to homework questions, . E Ask an Expert e Bundle: Differential Equations with Bou... < Chapter 11.1, Problem 12E > To show: The given functions are orthogonal and to find out the Problem 9E norm. Problem 10E Problem 11E Answer to Problem 12E Problem 12E The norm of the given functions are 1 ||= V2p, cos x ||= VP Problem 13E sin x ||= VP and Explanation of Solution Given: The given functions are {1, cos x, sin ".} for n = 1,2...m = 1,2.. in the interval [-p, p]. Calculation: плх Consider cos Mxx dx where n + m COS плх плх тлх cos mAx dx == 2 cos dx (1) cos COS -P Use the formula 2 cos A cos B = cos (A – B) + cos (A + B) cos mx dx = (п — т) лх . cos (п + m) лх cos cos + P p Now, integrate the right hand side of above equation. (n+m) (n-m)x sin плх cos MAX dx = sin 2(n+m)x Cos 2(n-m)x Privacy · Terms
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