TrigSteps - Maple Help
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Student[Basics]

 TrigSteps
 show steps in the simplification of a specified expression

 Calling Sequence TrigSteps(ex, opts)

Parameters

 ex - expression opts - options of the form keyword=value where keyword is one of displaystyle, output

Description

 • The TrigSteps command is used to show the steps of simplifying the trig functions in a basic student expression.
 • The fullsolution option can be used to show additional arithmetic steps in the simplification.
 • The displaystyle and output options can be used to change the output format.  See OutputStepsRecord for details.
 • This function is part of the Student:-Basics package.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right):$
 > $\mathrm{TrigSteps}\left(\mathrm{tan}\left(x\right)\mathrm{cos}\left(x\right)\right)$
 $\begin{array}{lll}{}& {}& \text{Let's simplify}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Apply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{Quotient}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{trig identity,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\mathrm{tan}{}\left(x\right)=\frac{\mathrm{sin}{}\left(x\right)}{\mathrm{cos}{}\left(x\right)}\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{sin}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right)}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{cos}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right)}{}{\mathrm{cos}}{}\left({x}\right)\\ \text{•}& {}& \text{Evaluate}\\ {}& {}& {\mathrm{sin}}{}\left({x}\right)\end{array}$ (1)
 > $\mathrm{TrigSteps}\left(3\mathrm{sin}\left(x\right)+2\mathrm{cos}\left(x\right)\mathrm{tan}\left(x\right)\right)$
 $\begin{array}{lll}{}& {}& \text{Let's simplify}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Apply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{Quotient}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{trig identity,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\mathrm{tan}{}\left(x\right)=\frac{\mathrm{sin}{}\left(x\right)}{\mathrm{cos}{}\left(x\right)}\\ {}& {}& {3}{}{\mathrm{sin}}{}\left({x}\right){+}{2}{}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{sin}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right)}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{cos}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right)}{}{\mathrm{cos}}{}\left({x}\right)\\ \text{•}& {}& \text{Evaluate}\\ {}& {}& {5}{}{\mathrm{sin}}{}\left({x}\right)\end{array}$ (2)
 > $\mathrm{TrigSteps}\left(\mathrm{sin}\left(x\right)\mathrm{sec}\left(x\right),\mathrm{output}=\mathrm{typeset}\right)$
 $\begin{array}{lll}{}& {}& \text{Let's simplify}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Apply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{Reciprocal Function}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{trig identity,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\mathrm{sec}{}\left(x\right)=\frac{1}{\mathrm{cos}{}\left(x\right)}\\ {}& {}& {\mathrm{sin}}{}\left({x}\right){}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{cos}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right)}\\ \text{•}& {}& \text{Apply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{Quotient}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{trig identity,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\frac{\mathrm{sin}{}\left(x\right)}{\mathrm{cos}{}\left(x\right)}=\mathrm{tan}{}\left(x\right)\\ {}& {}& \left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{tan}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right)\right)\end{array}$ (3)
 > $\mathrm{TrigSteps}\left(\mathrm{sin}\left(x+{\mathrm{sin}\left(x\right)}^{2}+{\mathrm{cos}\left(x\right)}^{2}\right)\mathrm{csc}\left(x+1\right),\mathrm{mode}=\mathrm{Learn}\right)$
 $\begin{array}{lll}{}& {}& \text{Let's simplify}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Apply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{Reciprocal Function}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{trig identity,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\mathrm{csc}{}\left(x+1\right)=\frac{1}{\mathrm{sin}{}\left(x+1\right)}\\ {}& {}& {\mathrm{sin}}{}\left({x}{+}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}{+}{{\mathrm{cos}}{}\left({x}\right)}^{{2}}\right){}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{sin}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}\right)}\\ \text{•}& {}& \text{Apply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{Pythagoras}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{trig identity,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\mathrm{sin}{}\left(x\right)}^{2}=1-{\mathrm{cos}{}\left(x\right)}^{2}\\ {}& {}& \frac{{\mathrm{sin}}{}\left({x}{+}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{-}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{cos}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right)}^{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}}\right){+}{{\mathrm{cos}}{}\left({x}\right)}^{{2}}\right)}{{\mathrm{sin}}{}\left({x}{+}{1}\right)}\\ \text{•}& {}& \text{Evaluate}\\ {}& {}& {1}\end{array}$ (4)

Compatibility

 • The Student[Basics][TrigSteps] command was introduced in Maple 2022.
 • For more information on Maple 2022 changes, see Updates in Maple 2022.