I'm not sure how you guys are making nice equations on the board.
By using LaTeX (pronounced "LAY-teck"). You can find a quickie reference
here.
So I will attach the equation I did in microsoft word.
\(\displaystyle \dfrac{2\, +\, \tan^2(x)}{\sec^2(x)}\, -\, 1\, =\)
\(\displaystyle \dfrac{2\, +\, \left( \dfrac{\sin(x)} {\cos(x)} \right)^2} {\left( \dfrac{1} {\cos(x)} \right)^2} \, -\, 1\, =\)
\(\displaystyle 2\, +\, \left(\dfrac{\sin(x)}{\cos(x)}\right)^2\, \cdot\, \left(\dfrac{\cos(x)}{1}\right)\, -\, 1\, =\)
Then I'm not sure where to go with this.
I've formatted what you'd posted. Note that, as posted, you've changed the expression between the second and third lines of computations, because you left out the grouping, putting the "2+" as a separate thing (rather than being "joined" with the tangent fraction). Also, the square in the one denominator has disappeared. As a result, you've posted this:
\(\displaystyle 2\, +\, \left[\left(\dfrac{\sin(x)}{\cos(x)}\right)^2\, \cdot\, \left(\dfrac{\cos(x)}{1}\right)\right]\, -\, 1\, =\)
But you can't flip an expression that merely
contains fractions. You have to have a fractional term. So the first step would be to back up to the second line:
. . . . .\(\displaystyle \dfrac{2\, +\, \left( \dfrac{\sin(x)} {\cos(x)} \right)^2} {\left( \dfrac{1} {\cos(x)} \right)^2} \, -\, 1\)
...and then multiply out squares and convert to fractional-only form before flipping:
. . . . .\(\displaystyle \dfrac{\left(\dfrac{2\, \cos^2(x)}{\cos^2(x)}\, +\, \dfrac{\sin^2(x)}{\cos^2(x)}\right)}{\left(\dfrac{1}{\cos^2(x)}\right)}\, -\, 1\)
. . . . .\(\displaystyle \dfrac{\left(\dfrac{2\, \cos^2(x)\, +\, \sin^2(x)}{\cos^2(x)}\right)}{\left(\dfrac{1}{\cos^2(x)}\right)}\, -\, 1\)
. . . . .\(\displaystyle \left(\dfrac{2\, \cos^2(x)\, +\, \sin^2(x)}{\cos^2(x)}\right)\left(\dfrac{\cos^2(x)}{1}\right)\, -\, 1\)
...and so forth.
