Question

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

Answer 1

The answer is: `cos40`.

It is easy if we remember the angle difference formula of cosine, that says:

`cos(alpha-beta)=cosalphacosbeta+sinalphasinbeta`.

In this case `alpha=75` and `beta=35`, and we can use the formula conversely:

`cos75cos35+sin75sin35=cos(75-35)=cos40`.