What could educators do to motivate students to learn well in mathematics?

Mathematics is one of the most powerful tools to shape the way we think and see the world. But it's no secret that success in learning math is very much depends on maintaining a high level of motivation. Without motivation and a sense of emotional involvement, it's hard if not difficult to have the stamina to keep learning.

The question remains, what are the key factors that educators could do to motivate someone to learn mathematics? To what extent can educators could do?

One of the ways is to always encouraging students to be familiarized with some of the very handy mathematical formulas, just like the following one:

If $A,\, B,\,C$ are three angles from a triangle, i.e. $A+B+C=\pi$, then we should have known the following equality holds.

$\tan A +\tan B+\tan C=\tan A\tan B \tan C$

Knowing a little more enhance students' ability to solve for more challenging problems. When they are confident, they are motivated, thus, students with stronger motivation have a higher chance of continuing their study in mathematics and further their competence.

$A+B+C=\pi$

$A+B=\pi-C$

$\tan (A+B)=\tan (\pi-C)$

[MATH]\frac{\tan A+\tan B}{1-\tan A\tan B}=\frac{\tan \pi-\tan C}{1-\tan \pi\tan C}[/MATH]

[MATH]\frac{\tan A+\tan B}{1-\tan A\tan B}=\frac{0-\tan C}{1-(0)(\tan C)}[/MATH]

[MATH]\frac{\tan A+\tan B}{1-\tan A\tan B}=\frac{-\tan C}{1}[/MATH]

[MATH]\tan A+\tan B=(-\tan C)(1-\tan A\tan B)[/MATH]

[MATH]\tan A+\tan B=-\tan C+\tan A\tan B\tan C[/MATH]

[MATH]\tan A+\tan B+\tan C=\tan A\tan B\tan C[/MATH]

Can you now try to generate another relation between $A,\,B$ and $C$ for cotangent functions?