$tan(x)=+-\frac{sin(x)}{\sqrt[\phantom{2}]{1-si{n}^2(x)}}$

The following steps should be followed to show how these identities can be visualized:

In column B$,$ generate a series of X values from $-2$ to $2$ in increments of $0\mathrm{.}2($or $\frac{}{\frac{?}{?}}20).$

Either increment value will be fine.

In column C$,$ take the tangent of the values in Column B$.$

In column D$,$ perform the following calculation $+\frac{sin(x)}{\sqrt[\phantom{2}]{1-si{n}^2(x)}}$ where $x$ is the values in Column B$.$

Next, the two columns $($column C and D$)$ should be plotted on the same plot with the X values

from column B on the x $-$axis. Try to make the data points square for one set of data and circles

for the other, so you can see both sets of data.

Since the tangent function approaches $+$ and $-$ infinity, you will need to adjust the $y-$axis to a

maximum of $5$ and a minimum of $-5.$ Also, your graph should only present the data points, do

not connect the data points with a line. This causes the graph to get busy and puts a line in the

plot where there is actually a discontinuity.

The original equation above has a $+/-$sign before the Sine function. It should be seen from the

two plots that there are parts where the values on the right$-$hand side should be multiplied by $-1$

to fully meet the requirements of the identity. You should go to the rows in your data and update

the formula over this range such that the values in C and D match. Make sure when you do this,

you identify which rows you multiplied by $(-1)$ in the text box at the top of the worksheet along

with the corresponding range of X$-$values.

Make sure your plot has axis labels, a title and a legend with proper names $($not series $1$ and $2).$

To check your solution, the plots from Column C and Column D should completely overlap as

expected from the definition of an identity