Use trigonomeric identities to simplify the expression.
tan(-β)cos(β)=
-tan(β) cos(β)= -sinβ/cosβ * cosβ/1= -sinβ
my teacher worked this out, but I still don't understand, what formula was used to solve this?
The first step here is to change \(\displaystyle tan(-\beta)\) to \(\displaystyle -tan(\beta)\). This should be an identity you would have learned, which says that tan is an odd function.
The second step is to express everything in terms of sine and cosine; that is, to replace \(\displaystyle tan(\beta)\) with \(\displaystyle \dfrac{sin(\beta)}{cos(\beta)}\). This is called the quotient identity.
The third step is just algebra, multiplying two fractions.
If you have a list of identities, recognizing what your teacher did is just a matter of pattern matching: look for an identity that looks like what is being done. If you have trouble doing that, focus on what is changing from one step to the next.
If you don't have a list of identities, make one! Take all the identities you have learned and put them on one sheet of paper so you can see them all at once.
Reading work like this is an important skill, which comes before writing (that is, doing the simplification yourself). So you will want to look at examples in your textbook or online sites until you can follow what is being done.