Question

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

Answer 1

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.

Answer 2

Actually I take that back.

Answer 3

Cos squared - 1 all times 2 is cos of 2x

Answer 4

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.

Answer 5

Yes the trig identities are important here.

Answer 6

Thank you

Answer 7

Glad I could help :)

Answer 8

yo