TrigCombine Command

TrigCombine( <Expression> )

Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables.

Example: TrigCombine[sin(x) cos(3x)] gives {\frac{1}{2} sin \left( 4 x \right) - \frac{1}{2} sin \left( 2 x \right)}.

Example: TrigCombine[sin(x) + cos(x)] gives {\sqrt{2} cos \left( x - \frac{1}{4} \pi \right)} .

TrigCombine( <Expression>, <Target Function> )

Transforms a trigonometric expression including products of trigonometric functions into an expression without products involving sums of variables, preferring the given target function.

Example: TrigCombine[sin(x) + cos(x), sin(x)] gives {\sqrt{2} sin \left( x + \frac{1}{4} \pi \right)} .

Note: In the CAS View undefined variables can be used as well.

Example: TrigCombine[sin(p) cos(3p)] gives {\frac{1}{2} sin \left( 4 p \right) - \frac{1}{2} sin \left( 2 p \right)}.

Note: See also TrigExpand Command and TrigSimplify Command.