# Simplifying and expressing preferentially with cosines: trigcos

### 5.23.24 Simplifying and expressing preferentially with cosines: trigcos

Any trigonometric function can be written in terms of sins and coss, and with the identity sin(x)2+cos(x)2=1, the even powers of sin can be turned into powers of cos. The trigcos command performs these substitutions.

- trigcos takes one argument:
  expr, an expression containing trigonometric functions.
- trigsin(expr) returns expr with the trigonometric functions rewritten in terms of sin and cos, with as many sins as possible transformed to coss.

#### Example.

Input:

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

Output:

cos4x−cos2x+2