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)]

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)]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.3: The Addition And Subtraction Formulas

Problem 80E

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Question

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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)]

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