TrigExpand Command

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TrigExpand( <Expression> )
Transforms a trigonometric expression into an expression using only simple variables as arguments.
Example: TrigExpand(tan(x + y)) gives \mathrm{\mathsf{ \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 \mathrm{\mathsf{ \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 Mode evaluate.svg Evaluate mode gives \mathrm{\mathsf{ \frac{\frac{sin(x)}{cos(x)}+\frac{sin(y)}{cos(y)}} {1-\frac{sin(x)}{cos(x)} \cdot \frac{sin(y)}{cos(y)}} }}
in Mode numeric.svg Numeric mode gives \mathrm{\mathsf{ \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 Menu view cas.svg 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 \mathrm{\mathsf{ 2cos \left( \frac{x}{2} \right) sin \left( \frac{x}{2} \right) }}
  • TrigExpand(sin(x)/(1+cos(x)), tan(x), x/2) gives \mathrm{\mathsf{ 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 \mathrm{\mathsf{ tan \left( \frac{x}{2} \right) +tan \left( \frac{y}{2} \right) }}.


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