Twins? Is there any difference between the vector space spanned by the set {cos t, sin t}

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Twins? Is there any difference between the vector space spanned by the set {cos t, sin t} and the vector space spanned by the set S = {cos t + sin t, cos t - sin t}?
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Differential Equations and Linear Algebra

ISBN: 978-0131860612

2nd edition

Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West

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