cos 100º cos 10º + sin 100° sin 10°

To simplify the expression cos 100° cos 10° + sin 100° sin 10°, we can use the angle difference identity for cosine:

cos(a - b) = cos a cos b + sin a sin b

In this case, a = 100° and b = 10°:

cos(100° - 10°) = cos 90° = 0

Therefore, the given expression simplifies to 0.