Put the following equation of a line into slope intercept form simplif

How do I show that $\frac{{\cos }^{2}A}{{\cos }^{2}B}+\frac{{\cos }^{2}B}{{\cos }^{2}C}+\frac{{\cos }^{2}C}{{\cos }^{2}A}\ge 4({\cos }^{2}A+{\cos }^{2}B+{\cos }^{2}C)$?
$A,B,C$ be the angles of an acute triangle.
How should I approach this kind of "geometric inequalities"? I've considered substituting the cosines using the law of the cosines and then use the Ravi transformation to turn it into an algebraic one, but that seems too tedious and unlikely to yield any beautiful solution. Any hints will be appreciated!

I have been quite confused by the definition of functions and their uses. First of all can one define functions in a clear understandable way, with a clear explanation of their uses, how they work and what they do?
Also I have some specific questions regarding functionsLet me give you a examples:
Also I have some specific questions regarding functions
Let me give you a examples:
1. ${\displaystyle y=f\left(x\right)\Rightarrow }$ This is one of the main reasons I have difficulties understanding functions...
What does the above statement tell me, and if y is a function why do we use ${\displaystyle y=}$ at all for a formula like ${\displaystyle y=mx+b}$ would it be the same as writing ${\displaystyle f\left(x\right)=mx+b?}$
2. Something like ${\displaystyle y=x^2}$ is apparently a function... but where is the function name? Which is the input and which is the output?
3. Lastly another example: Let me suppose ${\displaystyle f=}$ distance ${\displaystyle f\left(t\right)=t^2}$
${\displaystyle f\left(2\right)=4\Rightarrow }$ Does this mean distance is 4... which is the input which is the output?
Mainly what I'm looking for in an answer is a clear and 'easy' explanation with examples to help me understand this new topic

${\displaystyle 10\frac{1}{4}-5\frac{1}{3}=?}$ Solve and leave answer in reduced fractional format, no improper fractions.

How do you simplify ${\displaystyle \frac{5}{12}+\frac{2}{3}}$?

${\displaystyle \frac{1}{2}}$ divided by ${\displaystyle \frac{3}{5}}$

Reduce 9+6*3+5*8-7.

Solve the equation below with factoring. Separate multiple solutions with a comma any reduce and fractions.
${\displaystyle 4x^2-2x=x^2+8}$
${\displaystyle x=?}$