Find the value of
cos100°.cos40°+ sin100°.sin40°.

Correct option is D

Formula Used:

$$\cos A \cos B + \sin A \sin B = \cos(A - B)$$​

Solution:
In this case, A = 100° and B = 40°, so we apply the identity:
​$$\cos 100^\circ \cos 40^\circ + \sin 100^\circ \sin 40^\circ \\= \cos(100^\circ - 40^\circ)\\= \cos 60^\circ$$​​
We know that $$\cos 60^\circ = \frac{1}{2}$$​

​$$\cos 100^\circ \cos 40^\circ + \sin 100^\circ \sin 40^\circ = \frac12\\$$​​