TrigExpand Command

TrigExpand[ <Expression> ]

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

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

TrigExpand[ <Expression> ]

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

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

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.