Answer
$$\sqrt{\frac{1+\cos76^\circ}{2}}=\cos38^\circ$$
Work Step by Step
$$X=\sqrt{\frac{1+\cos76^\circ}{2}}$$
Recall the half-angle identity for cosine, which states
$$\sqrt{\frac{1+\cos A}{2}}=\cos\frac{A}{2}$$
So we can apply the identity to $X$ with $A=76^\circ$, meaning that
$$X=\sqrt{\frac{1+\cos76^\circ}{2}}=\cos\frac{76^\circ}{2}$$
$$X=\cos38^\circ$$
Therefore, $$\sqrt{\frac{1+\cos76^\circ}{2}}=\cos38^\circ$$
$\cos38^\circ$ is a single trigonometric function, so we can stop here.
