Question
Show that $f$ and $g$ are orthogonal in the inner product space $C[a, b]$ with the inner product$$\langle f, g\rangle=\int_{a}^{b} f(x) g(x) d x$$$$C[-\pi / 2, \pi / 2], \quad f(x)=\cos x, \quad g(x)=\sin x$$
Step 1
The inner product is defined as: $$\langle f, g\rangle=\int_{a}^{b} f(x) g(x) d x$$ where $a = -\pi/2$ and $b = \pi/2$. Show more…
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