TrigExpand Command

TrigExpand[ <Expression> ]

Transforms a trigonometric expression into an expression using only simple variables as arguments.

Example: TrigExpand[tan(x + y)] gives \frac{\frac{sin(x)}{cos(x)}+\frac{sin(y)}{cos(y)}} {1-\frac{sin(x)}{cos(x)} \cdot \frac{sin(y)}{cos(y)}} .

TrigExpand[ <Expression>, <Target Function> ]

Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function.

Example: TrigExpand[tan(x + y), tan(x)] gives \frac{-tan(x) - tan(y)}{tan(x) tan(y) - 1}.

CAS Syntax

CAS syntaxes may show different results, depending on the selected output mode:

Example: TrigExpand[tan(x + y)]
in Evaluate mode gives \frac{\frac{sin(x)}{cos(x)}+\frac{sin(y)}{cos(y)}} {1-\frac{sin(x)}{cos(x)} \cdot \frac{sin(y)}{cos(y)}}
in Numeric mode gives \frac{sin(x) cos(y) + sin(y) cos(x)}{- sin(x) sin(y) +cos(x) cos(y) } .

The following commands are only available in the CAS View:

TrigExpand[ <Expression>, <Target Function>, <Target Variable> ]

Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function and target variable.

Example: TrigExpand[sin(x), sin(x), x/2] gives 2cos \left( \frac{x}{2} \right) sin \left( \frac{x}{2} \right) .

Example: TrigExpand[sin(x)/(1+cos(x)), tan(x), x/2] gives tan \left( \frac{x}{2} \right).

TrigExpand[ <Expression>, <Target Function>, <Target Variable>, <Target Variable> ]

Transforms a trigonometric expression into an expression using only simple variables as arguments, preferring the given target function and target variables.

Example: TrigExpand[csc(x) - cot(x) + csc(y) - cot(y), tan(x), x/2, y/2] gives tan \left( \frac{x}{2} \right) +tan \left( \frac{y}{2} \right) .

Note: See also TrigSimplify Command and TrigCombine Command.