Answer
$$\sqrt{\frac{1-\cos40^\circ}{2}}=\sin20^\circ$$
Work Step by Step
$$X=\sqrt{\frac{1-\cos40^\circ}{2}}$$
Recall the half-angle identity for sine, which states
$$\sqrt{\frac{1-\cos A}{2}}=\sin\frac{A}{2}$$
So we can apply the identity to $X$ with $A=40^\circ$, meaning that
$$X=\sqrt{\frac{1-\cos40^\circ}{2}}=\sin\frac{40^\circ}{2}$$
$$X=\sin20^\circ$$
Therefore, $$\sqrt{\frac{1-\cos40^\circ}{2}}=\sin20^\circ$$
$\sin20^\circ$ is a single trigonometric function, so we can stop here.
