Answer
$$\dfrac{\sqrt 3}{2}$$
Work Step by Step
Apply the difference formula:
$\cos(A-B)=\cos(A)\cos(B)+\sin(A)\sin(B)$
Therefore,
$$\cos(40^\circ) \ \cos(10^\circ) +\sin(40^\circ) \ \sin(10^\circ)\\
=\cos \ (40^\circ -10^\circ)\\
=\cos \ (30^\circ)\\
=\dfrac{\sqrt 3}{2}$$
