# How do you write cos75cos35+sin75sin 35 as a single trigonometric function?

The answer is: $\cos 40$.
$\cos \left(\alpha - \beta\right) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$.
In this case $\alpha = 75$ and $\beta = 35$, and we can use the formula conversely:
$\cos 75 \cos 35 + \sin 75 \sin 35 = \cos \left(75 - 35\right) = \cos 40$.