TrigCombine Command

TrigCombine( <Expression> )

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

Examples:

  • 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> )

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

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

Notes:

  • In the Menu view cas.svg CAS View undefined variables can be used as well.

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