TrigExpand Command

TrigExpand( <Expression> ): Transforms a trigonometric expression into an expression using only simple variables as arguments.

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

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.

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:

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.

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