what does the expression cos 40°cos10°+sin40°sin10° equal?

We'll recognize the
identity:

cos(x-y)=cos x*cos y + sin x*sin
y

Let x = 40 and y = 10

The
given sum could be written:

cos 40*cos 10 + sin 40*sin 10 =
cos (40 - 10)

cos 40*cos 10 + sin 40*sin 10 = cos
30

But cos 30 = (sqrt
3)/2

The given sum is equal to: cos 40*cos 10
+ sin 40*sin 10 = (sqrt 3)/2.