Chapter 6 - Vector Spaces - 6.2 Linear Independence, Basis, and Demension - Exercises for 6.2 - Page 457: 11

This set is not linearly independent. $1\cdot1+(-1)\sin^2(x)=\cos^2(x)$

Since $1 + (-1)\sin^2(x) = \cos^2(x)$, $\cos^2(x)$ can be written as a linear combination of the other vectors. Thus, the set of functions are not linearly independent.