Answer
The statement does not make sense.
Work Step by Step
We know that this statement does not make sense because to calculate the value of $\cos 100{}^\circ $ using the half angle formula, it is required to know the value of $\cos 200{}^\circ $.
$\begin{align}
& \cos \frac{\alpha }{2}=\pm \sqrt{\frac{1+\cos \alpha }{2}} \\
& \cos \frac{200{}^\circ }{2}=\pm \sqrt{\frac{1+\cos 200{}^\circ }{2}} \\
& \cos 100{}^\circ =\pm \sqrt{\frac{1+\cos 200{}^\circ }{2}}
\end{align}$
Clearly, the value of $\cos 200{}^\circ $ can be computed with the help of the calculator but there is no known trigonometric value of $200{}^\circ $ angle.
