1. ## Find an expression

hmmm...so i need to find an expression for the attached image...
im getting tan((x^2-4)/4) but its wrong, what am I missing?

hmmm...so i need to find an expression for the attached image...
im getting tan((x^2-4)/4) but its wrong, what am I missing?

Let $\alpha = \cos^{-1} \left( \frac{2}{x} \right) \Rightarrow \cos \alpha = \frac{2}{x}$. So you want the value of $\tan^2 \alpha$.

Now note that $\tan^2 \alpha = \frac{1}{\cos^2 \alpha} - 1$. Make the necessary substitution and simplify.

3. o ya srry,,, it says in terms of x so that doesn't work i think and it said yo use as a hint: tan^(2)+1=sec^2(x)

Am I to understand that you cannot (or haven't tried to) substitute $\cos \alpha = \frac{2}{x}$ into the right hand side of $\tan^2 \alpha = \frac{1}{\cos^2 \alpha} - 1$ ?