## anonymous 5 years ago F=cos^2 (x) g=sin^2 (x) Does cos(2x) lie in the space spanned by f & g?

1. anonymous

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

Actually I take that back.

3. anonymous

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

4. anonymous

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

Yes the trig identities are important here.

6. anonymous

Thank you

7. anonymous