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.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right)\:$

$\mathrm{TrigSteps}\left(\tan \left(x\right)\cos \left(x\right)\right)$

$\begin{array}{lll}& & \text{Let's simplify}\\ & & \tan \left(x\right)\cdot \cos \left(x\right)\\ \text{•}& & \text{Apply}\text{Quotient}\text{trig identity,}\tan \left(x\right)=\frac{\sin \left(x\right)}{\cos \left(x\right)}\\ & & \frac{\sin \left(x\right)}{\cos \left(x\right)}\cos \left(x\right)\\ \text{•}& & \text{Evaluate}\\ & & \sin \left(x\right)\end{array}$

$\mathrm{TrigSteps}\left(3\sin \left(x\right)+2\cos \left(x\right)\tan \left(x\right)\right)$

$\begin{array}{lll}& & \text{Let's simplify}\\ & & 3\cdot \sin \left(x\right)+2\cdot \tan \left(x\right)\cdot \cos \left(x\right)\\ \text{•}& & \text{Apply}\text{Quotient}\text{trig identity,}\tan \left(x\right)=\frac{\sin \left(x\right)}{\cos \left(x\right)}\\ & & 3\sin \left(x\right)+2\frac{\sin \left(x\right)}{\cos \left(x\right)}\cos \left(x\right)\\ \text{•}& & \text{Evaluate}\\ & & 5\sin \left(x\right)\end{array}$

$\mathrm{TrigSteps}\left(\sin \left(x\right)\sec \left(x\right)\,\mathrm{output}=\mathrm{typeset}\right)$

$\begin{array}{lll}& & \text{Let's simplify}\\ & & \sin \left(x\right)\cdot \sec \left(x\right)\\ \text{•}& & \text{Apply}\text{Reciprocal Function}\text{trig identity,}\sec \left(x\right)=\frac{1}{\cos \left(x\right)}\\ & & \sin \left(x\right)\frac{1}{\cos \left(x\right)}\\ \text{•}& & \text{Apply}\text{Quotient}\text{trig identity,}\frac{\sin \left(x\right)}{\cos \left(x\right)}=\tan \left(x\right)\\ & & \left(\tan \left(x\right)\right)\end{array}$

$\mathrm{TrigSteps}\left(\sin \left(x+{\sin \left(x\right)}^2+{\cos \left(x\right)}^2\right)\csc \left(x+1\right)\,\mathrm{mode}=\mathrm{Learn}\right)$

$\begin{array}{lll}& & \text{Let's simplify}\\ & & \sin \left(x+{\sin \left(x\right)}^2+{\cos \left(x\right)}^2\right)\cdot \csc \left(x+1\right)\\ \text{•}& & \text{Apply}\text{Reciprocal Function}\text{trig identity,}\csc \left(x+1\right)=\frac{1}{\sin \left(x+1\right)}\\ & & \sin \left(x+{\sin \left(x\right)}^2+{\cos \left(x\right)}^2\right)\frac{1}{\sin \left(x+1\right)}\\ \text{•}& & \text{Apply}\text{Pythagoras}\text{trig identity,}{\sin \left(x\right)}^2=1-{\cos \left(x\right)}^2\\ & & \frac{\sin \left(x+\left(1-{\cos \left(x\right)}^2\right)+{\cos \left(x\right)}^2\right)}{\sin \left(x+1\right)}\\ \text{•}& & \text{Evaluate}\\ & & 1\end{array}$

The Student[Basics][TrigSteps] command was introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.