Is the set {sin nx , cos mx} an orthogonal set with respect to the inner product on the set of all continuous real-valued functions given by (f, g) = S",fg dt ? Justify your answer. 9. Note: 1- cos(2x) sin²x = cos?x = 1+ cos(2x) sin A cos B = =[sin(A – B) + sin(A+B)]

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Is the set {sin nx , cos mx} an orthogonal set with respect to the inner product on the set of all continuous
real-valued functions given by (f, g) = S",f g dt ? Justify your answer.
9.
Note:
1 - cos(2x)
1+ cos(2x)
sin²x =
cos²x =
2
sin A cos B = = (sin(A – B) + sin(A +B)]
sin A sin B =
[cos(A – B) – cos(A + B)]
cos A cos B = =[cos (A – B) + cos(A+ B)]
Transcribed Image Text:Is the set {sin nx , cos mx} an orthogonal set with respect to the inner product on the set of all continuous real-valued functions given by (f, g) = S",f g dt ? Justify your answer. 9. Note: 1 - cos(2x) 1+ cos(2x) sin²x = cos²x = 2 sin A cos B = = (sin(A – B) + sin(A +B)] sin A sin B = [cos(A – B) – cos(A + B)] cos A cos B = =[cos (A – B) + cos(A+ B)]
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