Hello AquafinaThe function gives the area between any two tangents and the circle expressed as a function of , the angle between the tangents.

So if we denote the angle between the tangents from to the circle by , then the area between these tangents and the circle is . But this area is given by . Hence .

But, from . Therefore . We can replace by any other parameter; in particular by . So .

For part (iii) I should do as you have done. The calculation is very straightforward for . Why complicate it?

Grandad