Answer
No, $\sin(2x)$ is not in the span of $f(x)$ and $g(x)$..
Work Step by Step
Since it is impossible to write $\sin(2x) = a\sin^2(x) + b\cos^2(x)$ for all $a,b \in \mathbb{R}$, $\sin(2x)$ is not in the span of $f(x)$ and $g(x)$.
Linear Algebra: A Modern Introduction
by Poole, David
Published by
Cengage Learning
ISBN 10:
1285463242
ISBN 13:
978-1-28546-324-7
Chapter 6 - Vector Spaces - 6.1 Vector Spaces and Subspaces - Exercises for 6.1 - Page 443: 57
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