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anonymous

  • 5 years ago

F=cos^2 (x) g=sin^2 (x) Does cos(2x) lie in the space spanned by f & g?

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  1. anonymous
    • 5 years ago
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    Sure since 1 and \[\cos^2x\] are both in the space, 1/2 times (1+ \[\cos^2x\]) which is cos of 2x is in the space.

  2. anonymous
    • 5 years ago
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    Actually I take that back.

  3. anonymous
    • 5 years ago
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    Cos squared - 1 all times 2 is cos of 2x

  4. anonymous
    • 5 years ago
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    So it is a matter of using the trig identity for cos2x. Then seeing that it is a linear combination of 1 and cos^2 (x) which are both in the space.

  5. anonymous
    • 5 years ago
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    Yes the trig identities are important here.

  6. anonymous
    • 5 years ago
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    Thank you

  7. anonymous
    • 5 years ago
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    Glad I could help :)

  8. anonymous
    • 5 years ago
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    yo

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