Answer
see the proof below.
Work Step by Step
Let $f(x)=\cos x, g(x)=\sin x $, $C[-\frac{\pi}{2},\frac{\pi}{2},]$
\begin{aligned}\langle f,g\rangle &=\int_{-\frac{\pi}{2},}^{\frac{\pi}{2}}\cos x \sin x d x\\ &=\int_{-\frac{\pi}{2},}^{\frac{\pi}{2}}\sin x d\sin x \\
&=\left[\frac{1}{2}\sin^2x\right]_{-\frac{\pi}{2},}^{\frac{\pi}{2}} \\ &=0 \end{aligned}.
then $f$ and $g$ are orthogonal in the inner product space $C[-\frac{\pi}{2},\frac{\pi}{2},]$.