Mathematica Sec and Csc

Question

How can I prevent Mathematica from using the "old fashioned" functions "Sec" and "Csc"?

In Germany these functions are "old fashioned" as they are not taught anymore at school.

Answer 1

According to this MathGroup post, it's possible to get rid of the superfluous Csc and Sec by doing the following:

Unprotect[Csc, Sec];
Format[Csc[x_]] := HoldForm[1/Sin[x]];
Format[Sec[x_]] := HoldForm[1/Cos[x]];
Protect[Csc, Sec];

That old solution at least gives you the following:

Csc[t]

$\frac{1}{\sin(t)}$

Sec[t]

$\frac{1}{\cos(t)}$

but it still won't be able to print out

$\frac{1}{\cos^2(t)}$

if you type in Sec[t]^2. Instead you get

$\left(\frac{1}{\cos(t)}\right)^2$

But maybe that's OK for your taste. If not, then Mr. Wizard's solution is better because it does put the square in the denominator.

Answer 2

This is similar to my Log question and similar methods can be used.

$PrePrint = # /. {
     Csc[z_] :> 1 / Defer@Sin[z],
     Sec[z_] :> 1 / Defer@Cos[z]
  } &;

Example:

(x + y) Csc[x] Sec[y]

(x + y)/(Cos[y] Sin[x])