TrigCombine Command

TrigCombine( <Expression> ): Combines products of trigonometric terms into sums, or combines sums of trigonometric terms into an expression containing only a trigonometric function.

TrigCombine(sin(x) cos(3x)) gives $\frac{1}{2} \sin \left( 4 x \right) - \frac{1}{2} \sin \left( 2 x \right)$
TrigCombine(sin(x) + cos(x)) gives $\sqrt{2} \cos \left( x - \frac{1}{4} \pi \right)$ .

TrigCombine( <Expression>, <Target Function> ): Combines the terms of a trigonometric expression into an equivalent expression, containing only the given target function.

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

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

TrigCombine(sin(p) cos(3p)) gives $\frac{1}{2} \sin \left( 4 p \right) - \frac{1}{2} \sin \left( 2 p \right)$ .

See also TrigExpand Command and TrigSimplify Command.