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mutual orthogonality

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Solve problem described in the attached file.

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Solution Summary

This solution checks the mutual orthogonality within this case.

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Note: For question (a), there must be in the statement of problem or , which means that orthogonality of fn and gm holds only on a full period of functions "sinx" and "cosx".

a) It is said that two functions are orthogonal on L2 (-, ) if
( 1)
We will check this for the given functions:

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