# Simplifying and expressing preferentially with tangents: trigtan

### 5.23.25 Simplifying and expressing preferentially with tangents: trigtan

The trigtan command rewrites trigonometric expressions into expressions where as many trigonometric functions as possible are written in terms of tangents, using the identities sin(x)2+cos(x)2=1, tan(x)=sin(x)/cos(x).

- trigtan takes one argument:
  expr, an expression containing trigonometric functions.
- trigtan(expr) returns expr with the trigonometric functions written as much as possible in terms of tangents.

#### Example.

Input:

trigtan(sin(x)^4+cos(x)^2+1)

Output:

2 tan4x+3 tan2x+2
tan4x+2 tan2x+1