tan^2a-1/1+tana

Yes, easy to overlook this, but it's always worth keeping an eye out for the difference of two squares, even when there isn't an explicit ² sign on the number 1. 

Since we are not given a value for the variable, "a", I assume we have to somehow simplify this expression.

tan^2a-1/1+tana = tan^(2a-1) / 1 + tan(a) OR tan^(2a) - 1 / 1 + tan(a) OR tan^(2)a - 1 / 1 + tan(a) OR tan^(2)(a-1) / 1 + tan(a). The first two possiblities are weird because the "2a" is a variable and is included in the power of the tan. The last one is unlikely leaving the third form, which is one that makes the most sense.

tan^(2)a - 1 / 1 + tan(a): Simplifying this is tricky since the "tan^(2)a" and "tan(a)" are both very different. We would need a bit more information such as a value for the variable, "a", or any other extra hints provided.

$$\frac{\tan^2a - 1}{1+\tan a }=\frac{(\tan a + 1)(\tan a -1)}{1+\tan a}=\tan a -1$$

Ohh, I see the simplification part now! Thanks, Alan! I overlooked splitting the numerator into two.