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
They are related through a right angled triangle where
$\displaystyle sin\theta = \frac{O}{H}$ , $\displaystyle cos\theta = \frac{A}{H}$ and $\displaystyle tan\theta = \frac{O}{A}$
where O, the opposite, is $\displaystyle 2t$
where A, the adjacent, is $\displaystyle 1-t^2$
and H, the hypotenuse, is $\displaystyle 1+t^2$
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?