Chapter 6.1, Problem 28E

To determine

To prove:

The set of functions $\left\{1,\cos x,\sin x,\mathrm{...},\cos nx,\sin nx\right\}$ where $n$ is a positive integer is linearly independent when $n=2$ in the interval $\left(a,b\right)=\left(-\infty ,\infty \right)$