# TrigExpand Command

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##### Command Categories (All commands)

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)}} .
It can also expand a product into a linear expression
Example: TrigExpand(sin(x)sin(x/3)) gives \frac{3}{2 \; x^{2}} \; cos \left( 2 \cdot \frac{x}{3} \right) - \frac{3}{2 \; x^{2}} \; cos \left( 4 \cdot \frac{x}{3} \right) .

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.
Examples:
• TrigExpand(sin(x), sin(x), x/2) gives 2cos \left( \frac{x}{2} \right) sin \left( \frac{x}{2} \right)
• 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) .

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