Question
Show that the functions $\cos \left(n+\frac{1}{2}\right) x, n=0,1,2, \cdots$, are orthogonal on $(0, \pi)$. Expand the function $f(x)=1$ on $(0, \pi)$ in terms of them.
Step 1
This means that the integral of the product of any two different functions over the interval $(0, \pi)$ is zero. Show more…
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