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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?
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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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sure 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually I take that back.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Cos squared  1 all times 2 is cos of 2x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes the trig identities are important here.
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