# Simplifying trigonometric expressions: trigsimplify

### 5.23.6 Simplifying trigonometric expressions: trigsimplify

The trigsimplify command simplifies trigonometric expressions by combining simplify (see Section 5.12.14), texpand (see Section 5.25.1), tlin (see Section 5.23.2), tcollect (see Section 5.23.4), trigsin (see Section 5.23.23), trigcos (see Section 5.23.24) and trigtan (see Section 5.23.25) commands in a certain order.

- trigsimplify takes one argument:
  expr, an argument containing trigonometric functions.
- trigsimplify(expr) returns the simplified form of expr.

#### Examples.

- Input:
  trigsimplify((sin(x+y)-sin(x-y))/(cos(x+y)+cos(x-y)))
  Output:

  tany

- Input:
  trigsimplify(1-1/4*sin(2a)^2-sin(b)^2-cos(a)^4)
  Output:

  sin2a−sin2b