question evaluate the expression below (for angles measured in radians). cos(cos^(-1)(sqrt(3)/2))

Explanation:

Step1: Recall inverse - cosine property

The function $y = \cos^{-1}(x)$ is the inverse of the cosine function $y=\cos(x)$ for $x\in[- 1,1]$ and $y\in[0,\pi]$. One of the fundamental properties of inverse - functions is that $\cos(\cos^{-1}(a))=a$ when $a\in[-1,1]$.

Step2: Check the value of the argument

The value of $a = \frac{\sqrt{3}}{2}$, and since $-1\leqslant\frac{\sqrt{3}}{2}\leqslant1$, we can apply the inverse - cosine property.

Answer:

$\frac{\sqrt{3}}{2}$