Show that the space spanned by B = {cos(x), sin(x)} is equivalent to the space spanned by B = {eix, e-ix}. (Hint: Show t

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Show That The Space Spanned By B Cos X Sin X Is Equivalent To The Space Spanned By B Eix E Ix Hint Show T 1 (25.83 KiB) Viewed 35 times

Show that the space spanned by B = {cos(x), sin(x)} is equivalent to the space spanned by B = {eix, e-ix}. (Hint: Show that any arbitrary element of span(B) can be written as a linear combination of the elements in B) (Hint: recall the identities sin(x) (1/2i) (ei - e-ir) and cos(x) = (1/2)(²x + e-ix))