Here I am trying to find the general solution to what is on top of the page. Have I done this correctly? Thanks if you can check this for me

2. You introduced t in the second line without explaining it's relation to $\theta$.

It would be better if you could explain how they are related

3. Originally Posted by e^(i*pi)
You introduced t in the second line without explaining it's relation to $\theta$.

It would be better if you could explain how they are related
They are related through a right angled triangle where

$sin\theta = \frac{O}{H}$ , $cos\theta = \frac{A}{H}$ and $tan\theta = \frac{O}{A}$

where O, the opposite, is $2t$
where A, the adjacent, is $1-t^2$
and H, the hypotenuse, is $1+t^2$

I missed out the explanation on this (which I think is best shown when the triangle is actually drawn out) but will keep it in mind whenever I do this type of question in the future.
Otherwise, would you believe that my working is correct?