Hi Lawson,

Lets go back to the second line of what you have done so far:

= 1 + (1- cos2x)/(1 - sin2x)

We can continue from above by looking at the equation as the addition of a whole number to a fraction. The whole number is the **1** and the fraction is **(1- cos2x)/(1 - sin2x).** Therefore we first need to convert the whole number to a fraction with the same denominator:

=> 1 + (1- cos^{2}x)/(1 - sin^{2}x)

= (1 - sin^{2}x)/(1 - sin^{2}x) + (1- cos^{2}x)/(1 - sin^{2}x) = [(1 - sin^{2}x) + (1 - cos^{2}x)]/ (1 - sin^{2}x)

Now if we replace all the 1s with cos^{2} + sin^{2}x, we will have:

[(cos^{2}x + sin^{2}x -
sin^{2}x) + (cos^{2}x + sin^{2}x -
cos^{2}x)]/ (cos^{2}x + sin^{2}x
- sin^{2}x)

= [cos^{2}x + sin^{2}x]/cos^{2}x

= 1/cos^{2}x

= **sec**^{2}x

Hope this helps!